MCAT physics chap 6 circuits 16%

when resistors are the same

" More generally, when n identical resistors are wired in parallel, the total resistance is given by R/n . Note that the voltage across each of the parallel resistors is equal and that, for equal resistances, the current flowing through each of the resistors is also equal (that is, a current of Itotl/n runs through each)."

uniform electric field

" The separation of charges sets up a uniform electric field between the plates with parallel field vectors" E=V/d from positive toward negative always

ohmeters

" an ohmmeter does not require a circuit to be active (in fact, some ohmmeters will give false readings or can be damaged by an active circuit). Ohmmeters will often have their own battery of known voltage and then function as ammeters through another point in the circuit. Because only one circuit element is being analyzed, Ohm's law can be used to calculate resistance by knowing the ohmmeter's voltage and the current created through another point in the circuit." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

properties of capacitors

" positive charge builds up on the plate connected to the positive (higher potential) terminal, and negative charge builds up on the plate connected to the negative (lower potential) terminal. The two-plate system is a capacitor because it can store a particular amount of charge at a particular voltage"

key concept uniform electric field

" the equation for E here can be derived from the other fundamental electrostatics equations. IfV= kQ/r and E=kQ/r^2 , then V = E × r. r in this setup is the distance between the plates, d, so we can rewrite this as V = Ed." .

current

" the flow of charge between two points at different electrical potentials connected by a conductor, such as a copper wire" I= Q/deltat Q= charge Si unit: ampere: 1A=1C/s

voltmeters

", requires a circuit to be active. Voltmeters also use magnetic properties of current-carrying wires. However, voltmeters are used to measure the voltage drop across two points in a circuit. They are wired in parallel to these two points. Because the goal with any meter is to minimize its impact on the rest of the circuit, and voltmeters are wired in parallel, an ideal voltmeter has infinite resistance." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"How does a dielectric material impact capacitance? Voltage? Charge?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A dielectric material will always increase capacitance. If the capacitor is isolated, its voltage will decrease when a dielectric material is introduced; if it is in a circuit, its voltage is constant because it is dictated by the voltage source. If a capacitor is isolated, the stored charge will remain constant because there is no additional source of charge; if it is in a circuit, the stored charge will increase." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

length

"According to the resistance equation, the resistance of a resistor is directly proportional to its length. A longer resistor means that electrons will have to travel a greater distance through a resistant material. This factor scales linearly: if a resistor doubles its length, it will also double its resistance." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"How does adding or removing a capacitor change the total capacitance of a circuit with capacitors in series? In parallel? Series: Parallel: "

"Adding a capacitor in series decreases the total capacitance of a circuit; removing one in series increases the total capacitance in the circuit. These relationships are reversed in parallel: adding a capacitor increases capacitance while removing one decreases it." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"How does adding or removing a resistor change the total resistance of a circuit with resistors in series? In parallel? Series: Parallel: " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Adding a resistor in series increases the total resistance of a circuit; removing one in series decreases the total resistance in the circuit. These relationships are reversed in parallel: adding a resistor decreases resistance while removing one increases it." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A circuit is set up with three resistors. The circuit has one branch through R1, then splits with R2 and R3 set up parallel to each other. If R1 = 3 Ω, R2 = 2 Ω, and R3 = 6 Ω, then what proportion of the total current will travel through each resistor? What will be the total resistance of the circuit?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"All current must travel through the first resistor, regardless of its resistance. Since the ratio of resistance for R2:R3 is 1:3, the ratio of current passing through them will be 3:1. In other words, of the current will pass through R2 while of the current will pass through R3. To calculate the total resistance, first calculate the resistance of the resistors in parallel:1/2+1/6- 2/3= 3/2=1.5 . Add this to the resistance of R1 to get the total resistance: 4.5 Ω." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

temperature

"Although not evident from the resistance equation, most conductors have greater resistance at higher temperatures. This is due to increased thermal oscillation of the atoms in the conductive material, which produces a greater resistance to electron flow. Because temperature is an intrinsic quality of all matter, we can think of the resistivity as a function of temperature. A few materials do not follow this general rule, including glass, pure silicon, and most semiconductors." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

key concept junction rule

"Kirchhoff's junction rule is just like a fork in a river. There are a certain number of water molecules in a river, and at any junction, that number has to go in one of the diverging directions; no water molecules spontaneously appear or disappear. The same holds true for the amount of current at any junction." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"What do each of the following types of meters measure? Where are they placed in circuits? What are their ideal resistances?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Meter Type Measures... Placement Ideal Resistance Ammeter Current In series with point of interest 0 Voltmeter Potential difference (voltage) Parallel with circuit element of interest ∞ Ohmmeter Resistance Two points in series with circuit element of interest 0" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

MCAT ex resistance

"On the MCAT, the most common resistors you will see outside of generic, unlabeled resistors are light bulbs, although all appliances function as resistors. You may also see resistance applied atypically, as in resistance to air flow in the lungs or to blood moving in the circulatory system. The same mathematical relationships will be useful in both circumstances." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"How does power relate to current, voltage, and resistance?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Power is related to current, voltage, and resistance through the equations P=IV=I^2R=V^2/R " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"What four physical quantities determine the resistance of a resistor?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Resistivity, length, cross-sectional area, and temperature all contribute to the resistance of a resistor." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

resistivity

"Some materials are intrinsically better conductors of electricity than others. For example, copper conducts electricity better than plastic, which is why electrical wires have a copper core surrounded by a layer of plastic rather than the other way around. The number that characterizes the intrinsic resistance to current flow in a material is called the resistivity (ρ), for which the SI unit is the ohm-meter (Ω · m)." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

What physical qualities contribute to the capacitance of a capacitor?

"Surface area, distance, and dielectric constant all contribute to the capacitance of a capacitor." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Assuming the plates are attached by a conducting material, how does a capacitor behave after the voltage source has been removed from a circuit?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The capacitor discharges, providing a current in the opposite direction of the initial current." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

CSA

"The equation for resistance also demonstrates an inverse proportionality between resistance and the cross-sectional area of the resistor: if a resistor's cross-sectional area is doubled, its resistance will be cut in half. This is because the increase in cross-sectional area increases the number of pathways through the resistor, called conduction pathways. The wider the resistor, the more current that can flow. This is analogous to a river, where the wider the river, the less resistance there is to water flow. Note, however, that electrical current does not follow the continuity equation that applies to incompressible fluids (A1ν1 = A2ν2); it instead obeys Kirchhoff's laws. " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

key concept resistors in series

"When there is only one path for the current to take, the current will be the same at every point in the line, including through every resistor. Once you know the current of the whole circuit, you can use V = IR to solve for the voltage drop across each resistor (assuming you know the resistances of the resistors)." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

resistance in resistors in paralellel

"While the voltage is the same for all parallel pathways, the resistance of each pathway may differ. In this case, electrons prefer the path of least resistance; in other words, the current will be largest through the pathways with the lowest resistance. In fact, there is an inverse relationship between the portion of the current that travels through a particular pathway and the resistance offered by that pathway. " 1/Rp= 1/R1 + 1/R2 + 1/R3 +1/R4 +1/Rn Rp will always decrease as more resistors are added

capacitor

An electrical device used to store electrical charge. defibulator, lets it loose as a gomo-gomo-no jet culveran

potential energy stored in capacitor

U=1/2CV^2

Capacitors in Parallel

C=C₁+C₂+C₃+... "Just as we saw with resistors in parallel, the voltage across each parallel capacitor is the same and is equal to the voltage across the source."

capacitance

C=Q/V, in Farads, 1 F=1C/V very large usually given in microfarads (1uF= 1 e-6) or pico farads: )pF= 1e-12) different from frday constant, which is 1e5

current 2

Charge: flow of electrons e- flow from lower electrical potential to higher electrical potential _neg to pos) direction of current is opposite: hiher ele pot to lower direct current: one direction, as seen in batteries and MCAT alternating current: changes periodically, as seen in building sized deer demons

Power

P=W/t=chsnge in energy/t P=IV= I^2R=V^2/R "where I is the current through the resistor, V is the voltage drop across the resistor, and R is the resistance of the resistor. Note that these different versions of the power equation can be interconverted by substitution using Ohm's law (V = IR)." MEMORIZE THESE

resistance of a resistor

R = pL/A "where ρ is the resistivity, L is the length of the resistor, and A is its cross-sectional area. " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

resistors in series

R=R₁+R₂+R₃+... current must pass through "As the electrons flow through each resistor, energy is dissipated, and there is a voltage drop associated with each resistor. The voltage drops are additive; that is, for a series of resistors, R1, R2, R3, ⋯ Rn, the total voltage drop will be Vs = V1 + V2 + V3 + ⋯ + Vn " "The set of resistors wired in series can be treated as a single resistor with a resistance equal to the sum of the individual resistances, termed the equivalent or resultant resistance. Note that Rs will always increase as more resistors are added."

important note for resistors in paralell

after getting sum of resistance, flip it so you geet R and not 1/R

dielectrics in circuit capacitors

charge on capacitor increases voltage stays constant, must be equal to voltage source "By increasing the amount of charge stored on the capacitor, the dielectric has increased the capacitance of the capacitor by a factor of the dielectric constant. "Thus, when a dielectric material is introduced into a circuit capacitor, the increase in capacitance arises from an increase in stored charge." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

resistors in parallel

common high potential terminal and common low potential allows charge to flow in different parrallel paths electrons can choose a path, however voltage drop is the same in each division

potential difference

current x resistance also voltage "can be produced by an electrical generator, a galvanic (voltaic) cell, a group of cells wired into a battery, or—as seen in classic science fair projects—even a potato." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

electrolytic conductivity

dpends on strnegth of solution deoiniszed water poor conductor and more likely a resistor OJ and sea water great conductors measured by voltage changes across solution ionic concentrations and conductivity directly related conductivity in onionic sol alwys lower than ionic solutions "While the concentration of total dissolved solids does relate to conductivity, the contribution of nonionic solids is much, much less important than ion concentration."

current

flow of positive charge equal and opposite of electron charge

electircal condictors

free flow of electric charge

capacitance of paralell plate dependant of

geometry: C=Eo (A/d) "where ε0 is the permittivity of free space 8.85e-12F/m A is the area of overlap of the two plates, and d is the separation of the two plates."

when cells aren't driving urrent

internal resistance is 0, voltage =EMF

example of resistors

light bulbs, coils in toaster, "The coils turn red-hot when the toaster is powered on and dissipate thermal energy, which is a direct consequence of the resistance that the coils pose to the current running through them." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

conductivity

metallic: solid metals and molten forms of slats electrolytic conductivty: solutions

emf is

pressure gradient

conductance

reciprocal of resistance units: siemens, S/m ease at which a particular material will allow current flow (mho)

metallic bond:

sea of electorns passing over flat and rigid metal cations metals make good conductrs

resistance

the opposition to the flow of electric charge basically friction, air resistance, motion is being opposed conductors: almost no resistance high resistance: insulators conductive materials that off resistance between 2 extremes called resistors

kirchoff's loop rule

"Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops. This is a consequence of the conservation of energy. All the electrical energy supplied by a source gets fully used up by the other elements within that loop. No excess energy appears, and no energy disappears that cannot be accounted for. Of course, energy can be changed from one form to another, so the kinetic energy of the electrons can be converted to thermal energy, light, or sound by the particular apparatus that is connected to the circuit. Remember that although Kirchhoff's loop rule is a consequence of the law of conservation of energy, this law is in terms of voltage (joules per coulomb), not just energy (joules). This can be expressed mathematically as Vsource = Vdrop "

kiechoff's junction rule

"At any point or junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point. This is an expression of conservation of electrical charge and can be expressed as Iinto junction = Ileaving junction"

current ad resistors in paralell

"Because the voltage drop across any one circuit branch must be same as the voltage drops across each of the other parallel branches, we can see that the magnitude of the current in each branch will be inversely proportional to the resistance offered by each branch. This comes directly from Ohm's law. Thus, if a circuit divides into two branches and one branch has twice the resistance of the other, the one with twice the resistance will have half the magnitude of current compared to the other. Remember that the sum of the currents going into each division, according to Kirchhoff's junction rule, must equal the total current going into the point at which the current divides." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

actual voltage

"Conductive materials, such as copper wires, act as weak resistors themselves, offering some magnitude of resistance to current and causing a drop in electrical potential (voltage). Even the very sources of emf, such as batteries, have some small but measurable amount of internal resistance, rint. As a result of this internal resistance, the voltage supplied to a circuit is reduced from its theoretical emf value by some small amount. The actual voltage supplied by a cell to a circuit can be calculated from V = Ecell - irint Equation 6.6 where V is the voltage provided by the cell, Ecell is the emf of the cell, i is the current through the cell, and rint is its internal resistance."

"Define the following terms and provide their SI units. Current: Voltage: Electromotive force (emf): " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Current is the movement of positive charge through a conductive material over time and is given in ampères C/s . Voltage is a potential difference between two points and is given in volts J/C . Electromotive force (emf) refers to the potential difference of the voltage source for a circuit, usually a battery, and is given in volts. Conductivity is the reciprocal of resistance and is a measure of permissiveness to current flow; it is measured in siemens (S)." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

circuits

"Currents (and circuits in general) are governed by the laws of conservation. Charge and energy must be fully accounted for at all times and can be neither created nor destroyed. An electric circuit is a conducting path that usually has one or more voltage sources (such as a battery) connected to one or more passive circuit elements (such as resistors). Kirchhoff's laws are two rules that deal with the conservation of charge and energy within a circuit."

"True or False: A voltmeter and an ammeter should not be placed in the same circuit." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"False. Voltmeters and ammeters are designed to have minimum impact on a circuit; thus, they can be used together." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"True or False: The sum of the voltage sources in a circuit is equal to the sum of the voltage drops in that circuit." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"False. While the voltage sources and voltage drops are equal in any closed loop, this is not necessarily true for the entire circuit. For example, a 9 V battery that powers 10 light bulbs in parallel has a 9 V voltage source and a 9 V drop across each light bulb—a total of 90 V of drop across all of the light bulbs combined." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Consider two resistors wired in parallel with R1 = 5 Ω and R2 = 10 Ω. If the voltage across them is 10 V, what is the current through each of the two resistors?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"First, the current flowing through the whole circuit must be found. To do this, the equivalent resistance must be calculated:" 1/5 +1/10= 3/10 = 10/3ohms "Using Ohm's law to calculate the current flowing through the circuit gives" Ip=Vp/Rp=10V/10/3 ohms= 3A (total current between the 2 "Three amps flow through the combination of R1 and R2. Because the resistors are in parallel, Vp = V1 = V2 = 10 V. Apply Ohm's law to each resistor individually:" I1= 10v/5ohms= 2A I2= 10V/10ohms= 1A "As a check, note that Ip = 3 A = I1 + I2. More current flows through the smaller resistor. In particular, note that R1, with half the resistance of R2, has twice the current. Once Ip was found to be 3 A, the problem could have been solved by noting the ratio of the resistances of the two branches." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

key concept loop

"If all of the voltage wasn't "used up" in each loop of the circuit, then the voltage would build after each trip around the circuit, which is impossible." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

nemonic capacitors

"Incorporating the dielectric constant into Equation 6.14 reveals that capacitors are CAκεd with charge (C = Aκε0/d)." "A dielectric material can never decrease the capacitance; thus, κ can never be less than 1." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

MCAT ex units

"It is always good practice to be able to derive the units of a variable from equations you know. If you were to solve for resistivity (ρ) in the resistance equation, you'd end up with AR/L . Because A is in square meters, R is in ohms, and L is in meters, it simplifies to meters times ohms, which are the units for resistivity." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The voltage across the terminals of an isolated 3 µF capacitor is 4 V. If a piece of ceramic having dielectric constant κ = 2 is placed between the plates, find the new charge, capacitance, and voltage of the capacitor." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The introduction of a dielectric by itself has no effect on the charge stored on the isolated capacitor. There is no new charge, so the charge is the same as before. The charge stored is therefore given by Q′ = Q = CV = (3 µF)(4 V) = 12 µC By introducing a dielectric with a dielectric constant of 2, the capacitance of the capacitor is multiplied by 2 (C′ = κC). Hence, the new capacitance is 6 µF. Now, the new voltage across the capacitor can be determined:" V'= Q'/C'= 12uC/6uF= 2V

"Which likely has a higher conductivity: 1 M glucose or 0.25 M NaCl? Why?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The sodium chloride solution likely has a higher conductivity because it is a salt and will increase the ion content of water. Glucose does not dissociate, and therefore it has a near-zero impact on conductivity." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

dissipation of stored charge

"The stored energy in a capacitor is only useful if it is allowed to discharge. The charge can be released from the plates either by discharging across the plates or through some conductive material with which the plates are in contact. For example, capacitors can discharge into wires, causing a current to pass through the wires in much the same way that batteries cause current to move through a circuit. The paddles of the defibrillator machine, once charged, are placed on either side of a patient's heart that has gone into a life-threatening arrhythmia (such as ventricular fibrillation). " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Three wires (a, b, and c) meet at a junction point P, as shown below. A current of 5 A flows into P along wire a, and a current of 3 A flows away from P along wire b. What is the magnitude and direction of the current along wire c? " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The sum of currents entering P must equal the sum of the currents leaving P. Assume for now that Ic flows out of P. If we find that it is negative, then we know the current must be going the other direction (into P). Thus, a current of 2 A flows out of P along wire c." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A circuit is wired with one cell supplying 5 V in series with three resistors of 3 Ω, 5 Ω, and 7 Ω, also wired in series as shown below. What is the resulting voltage across and current through each resistor of this circuit, as well as the entire circuit?" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The total resistance of the resistors is Rs = R1 + R2 + R3 = 3 Ω + 5 Ω + 7 Ω = 15 Ω Now use Ohm's law to get the current through the entire circuit: Because everything is in series, this is also the current through each circuit element. Now, use Ohm's law for each of the resistors in turn. From a to b, the voltage drop across R1 is IR1 = (0.33 A)(3 Ω) = 1.0 V From b to c, the voltage drop across R2 is IR2 = (0.33 A)(5 Ω) = 1.67 V From c to d, the voltage drop across R3 is IR3 = (0.33 A)(7 Ω) = 2.33 V" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A 3 µF capacitor is connected to a 4 V battery. If a piece of ceramic having dielectric constant κ = 2 is placed between the plates, find the new charge, capacitance, and voltage of the capacitor." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"This question is very similar to the previous one, but the voltage is held constant here by a battery. Thus, the new voltage is still 4 V. By introducing a dielectric with a dielectric constant of 2, the capacitance of the capacitor is multiplied by 2 (C′ = κC). Hence, the new capacitance is 6 µF. Now, the new charge on the capacitor can be determined: Q′ = C′V′ = (6 µF)(4 V) = 24 µC" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"True or False: The internal resistance of a battery will lower the amount of current it can provide." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"True. The internal resistance will lower the available voltage for the circuit. Lowering the available voltage will also lower current for any given resistance." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"True or False: In a circuit, the number of electrons entering a point and leaving that point are the same." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"True. This is a restatement of Kirchhoff's junction rule" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

Voltage (Resistors in Parallel)

"Vp = V1 = V2 = V3 = ⋯ = Vn " "Remember Kirchhoff's loop rule: if every resistor is in parallel, then the voltage drop across each pathway alone must be equal to the voltage of the source."

secondary batteries

"When a cell is discharging, it supplies current, and the current flows from the positive, higher potential end of the cell around the circuit to the negative, lower potential end. Certain types of cells (called secondary batteries) can be recharged. When these batteries are being recharged, an external voltage is applied in such a way to drive current toward the positive end of the secondary battery. In electrochemical terms, the cell acts as a galvanic (voltaic) cell when it discharges and as an electrolytic cell when it recharges." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

MCAT exp circuit probs

"When approaching circuit problems, the first things you need to find are the total (circuit) values: the total voltage (almost always given as the voltage of the battery), the total (equivalent) resistance, and the total current. To find the total current, first find the total resistance of the circuit." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

electromotive force

"When no charge is moving between the two terminals of a cell that are at different potential values, the voltage is called the electromotive force (emf or ε). Do not be misled by this term, as emf is not actually a force; it is a potential difference (voltage) and, as such, has units of joules per coulomb 1V= 1 J/C —not newtons. It may be helpful to think of emf as a "pressure to move" that results in current, in much the same way that a pressure difference between two points in a fluid-filled tube causes the fluid to flow."

ammeters

"used to measure the current at some point within a circuit. Using an ammeter requires the circuit to be on, or the current will be 0 A. Ammeters are inserted in series where the current is being measured and use the magnetic properties of a current-carrying wire to cause a visible needle movement or a calibrated display of the current. If there is a particularly high current, this will overwhelm the ammeter, and a special low resistance shunt is used in parallel with the ammeter to allow a reading. Ideally, an ammeter will not change circuit mathematics when it is inserted into the circuit. To do so, it must have an extremely low resistance. Ideal ammeters have zero resistance and no voltage drop across themselves." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

dielectric material

-insulator (air, glass, plastic) -introduced b/w the plates of a capacitor - increases capacitance by a factor called dielectric constant (k) "The capacitance due to a dielectric material is C′ = κC Equation 6.17 where C′ is the new capacitance with the dielectric present and C is the original capacitance."

capacitors in series

1/C=1/C₁+1/C₂+... opposite of resistors "This is because the capacitors must share the voltage drop in the loop and therefore cannot store as much charge. Functionally, a group of capacitors in series acts like one equivalent capacitor with a much larger distance between its plates (in fact, with a distance equal to those of each of the series capacitors added together). This increase in distance, as seen earlier, means a smaller capacitance." "Note that for capacitors in series, the total voltage is the sum of the individual voltages, just like resistors in series." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"How many moles of electrons pass through a circuit containing a 100 V battery and a 2 Ω resistor over a period of 10 seconds? (Note: ) 5.18 × 10-3 moles 500 moles 5.18 × 103 moles 5.2 × 106 moles" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

A "To determine the moles of charge that pass through the circuit over a period of 10 s, we will have to calculate the amount of charge running through the circuit. Charge is simply current multiplied by time, and the current can be calculated using Ohm's law: V=IR and I=Q/t= Vt/R Q= 100V*10s/2amp Then, calculate the number of moles of charge that this represents by using the Faraday constant and approximating F as 500C (mol e-/10^5= 5e-3 This is closest to (A)." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"In the figure below, six currents meet at point P. What is the magnitude and direction of the current between points P and x? 2 A, toward x 2 A, toward P 10 A, toward x 10 A, toward P" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

A "Kirchhoff's junction rule states that the sum of all currents directed into a point is always equal to the sum of all currents directed out of the point. The currents directed into point P are 8 A, 2 A, and 3 A, so the sum is 13 A. The currents directed out of point P are 5 A and 6 A, so the total is 11 A. Because the two numbers must always be equal, an additional current of 2 A must be directed away from point P toward point x." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The energy stored in a fully charged capacitor is given by . In a typical cardiac defibrillator, a capacitor charged to 7500 V has a stored energy of 400 J. Based on this information, what is the charge on the capacitor in the cardiac defibrillator? 1.1 × 10−5 C 5 × 10−2 C 1.1 × 10−1 C 3.1 × 106 C" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

A C "Because the question is asking us to calculate the charge on the capacitor, use the formula Q = CV. We are given V = 7500 V and can calculate C from the formula for energy, U=1/2CV^2 = 1/2 (Q/V)V^2= QV/2 Q=2U/V= 2(400)/7500= 800/8000= .1 C : Thus, the charge is close to 0.1 C, which is closest to (C)." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A 10 Ω resistor carries a current that varies as a function of time as shown. How much energy has been dissipated by the resistor after 5 s? 40 J 50 J 120 J 160 J" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

A C "Power is energy dissipated per unit time; therefore, the energy dissipated is E = PΔt. In the five-second interval during which the resistor is active, it has a 2 A current for three of those seconds. The power dissipated by a resistor R carrying a current I is P = I2R. Therefore, the energy dissipated is E = I2RΔt = (2 A)2(10 Ω)(3 s) = 4 × 10 × 3 = 120 J" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A voltaic cell provides a current of 0.5 A when in a circuit with a 3 Ω resistor. If the internal resistance of the cell is 0.1 Ω, what is the voltage across the terminals of the battery when there is no current flowing? 0.05 V 1.5 V 1.505 V 1.55 V" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

A D "This question tests our understanding of batteries in a circuit. The voltage across the terminals of the battery when there is no current flowing is referred to as the electromotive force (emf or ε of the battery). However, when a current is flowing through the circuit, the voltage across the terminals of the battery is decreased by an amount equal to the current multiplied by the internal resistance of the battery. Mathematically, this is given by the equation V = ε - irint To determine the emf of the battery, first calculate the voltage across the battery when the current is flowing. For this, we can use Ohm's law: Because we know the internal resistance of the battery, the current, and the voltage, we can calculate the emf: The answer makes sense in the context of a real battery because its internal resistance is supposed to be very small so that the voltage provided to the circuit is as close as possible to the emf of the cell when there is no current running." given V, I, and ir, solve for e

"Each of the resistors shown carries an individual resistance of 4 Ω. Assuming negligible resistance in the wire, what is the overall resistance of the circuit? 16 Ω 8 Ω 4 Ω 3 Ω" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

A D "The resistance of the three resistors wired in series is equal to the sum of the individual resistances (12 Ω). This means that the circuit functionally contains a 12 Ω resistor and a 4 Ω resistor in parallel. To determine the overall resistance of this system, use the formula 1/12+1/4= 4/12= 3

"Given that R1 = 20 Ω, R2 = 4 Ω, R3 = R4 = 32 Ω, R5 = 15 Ω, and R6 = 5 Ω, what is the total resistance in the setup shown below? 0.15 Ω 6.67 Ω 16.7 Ω 60 Ω" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

B "The fastest way to tackle these kinds of questions is to simplify the circuit bit by bit. For example, notice that R3 and R4 are in parallel with each other and are in series with R2; similarly, R5 and R6 are in series. If we determine the total resistance in each branch, we will be left with three branches in parallel. To start, find the total resistance in the middle branch: 1/32+1/32= 2/32=16 (flip) Next, take a look at the total resistance in the bottom branch: R5+6 = R5 + R6 = 15 Ω + 5 Ω = 20 Ω The circuit can now be viewed as three resistors in parallel, each providing a resistance of 20 Ω. The total resistance in the circuit is thus 1/20+1/20+1/20=3/20=20/3=6/67 " Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"The resistance of two conductors of equal cross-sectional area and equal lengths are compared, and are found to be in the ratio 1:2. The resistivities of the materials from which they are constructed must therefore be in what ratio? 1:1 1:2 2:1 4:1" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

B "The resistance of a resistor is given by the formula Thus, there is a direct proportionality between resistance and resistivity. Because the other variables are equal between the two resistors, we can determine that if R1:R2 is a 1:2 ratio, then ρ1: ρ2 is also a 1:2 ratio." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A transformer is a device that takes an input voltage and produces an output voltage that can be either larger or smaller than the input voltage, depending on the transformer design. Although the voltage is changed by the transformer, energy is not, so the input power equals the output power. A particular transformer produces an output voltage that is 300 percent of the input voltage. What is the ratio of the output current to the input current? 1:3 3:1 1:300 300:1" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

B A "We are told that transformers conserve energy so that the output power equals the input power. Thus, Pout = Pin, or IoutVout = IinVin. There is therefore an inverse proportionality between current and voltage. If the output voltage is 300% of the input voltage (3 times its amount), then the output current must be of the input voltage. This can be represented as a 1:3 ratio." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Which of the following will most likely increase the electric field between the plates of a parallel plate capacitor? Adding a resistor that is connected to the capacitor in series Adding a resistor that is connected to the capacitor in parallel Increasing the distance between the plates Adding an extra battery to the system" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

B D "The electric field between two plates of a parallel plate capacitor is related to the potential difference between the plates of the capacitor and the distance between the plates, as shown in the formula The addition of another battery will increase the total voltage applied to the circuit, which, consequently, will increase the electric field. The addition of a resistor in series will increase the resistance and decrease the voltage applied to the capacitor, eliminating (A). Adding a resistor in parallel will not change the voltage drop across the capacitor and should not change the electric field, eliminating (B). Increasing the distance between the plates, (C), would decrease the electric field, not increase it." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"In the circuit below, what is the voltage drop across the resistor? 1/2 2/3 5 V 7.5 V" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

C "To determine the voltage drop across the resistor, start by calculating the total resistance in the circuit. For the resistors in parallel, the equivalent resistance is 1/Rp= 1/2 +3/2 = 1/2 after flipping The total resistance in the circuit is the sum of the remaining resistor and the equivalent resistance of the other two: 1/2 +1/2= 1 Now that we know the equivalent resistance, we can calculate the total current using Ohm's law: I=V/R= 10/1= 10 Finally, we can determine the voltage drop across the parallel resistors. The voltage drop across the 1/2 resistor must be 10A (1/2)= 5v Therefore, there must be a 5 V drop across both the 2/3 resistor and 2 Ω resistor, according to Kirchhoff's loop rule. Each of these resistors forms a complete loop in combination with the resistor and 10 V voltage source, and the net potential difference around any closed loop must be 0 V." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"Which of the following best characterizes ideal voltmeters and ammeters? Ideal voltmeters and ammeters have infinite resistance. Ideal voltmeters and ammeters have no resistance. Ideal voltmeters have infinite resistance, and ideal ammeters have no resistance. Ideal voltmeters have no resistance, and ideal ammeters have infinite resistance." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

C "While this is primarily a recall question, it should also be intuitive. Voltmeters are attempting to determine a change in potential from one point to another. To do this, they should not provide an alternate route for charge flow and should therefore have infinite resistance. Ammeters attempt to determine the flow of charge at a single point and should not contribute to the resistance of a series circuit; therefore, they should have no resistance." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"If the area of a capacitor's plates is doubled while the distance between them is halved, how will the final capacitance (Cf) compare to the original capacitance (Ci)? Cf = Ci Cf = 2Ci Cf = 4Ci" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

D "This question should bring to mind the equation where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates. From this equation, we can infer that doubling the area will double the capacitance, and halving the distance will also double the capacitance. Therefore, the new capacitance is four times larger than the initial capacitance." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"A charge of 2 μC flows from the positive terminal of a 6 V battery, through a 100 Ω resistor, and back through the battery to the positive terminal. What is the total potential difference experienced by the charge? 0 V 0.002 V 0.2 V 6 V" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

D A "Kirchhoff's loop rule states that the total potential difference around any closed loop of a circuit is 0 V. Another way of saying this is that the voltage gained in the battery (6 V) will be used up through the resistors. Because this charge both started and ended at the positive terminal, its total potential difference is therefore 0 V. 6 V, (D), is the voltage gained in the battery as well as the voltage drop in the resistors—creating a net sum of 0 V." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

"If a defibrillator passes 15 A of current through a patient's body for 0.1 seconds, how much charge goes through the patient's skin? 0.15 C 1.5 C 15 C 150 C" Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

D B "Electrical current is defined as charge flow, or in mathematical terms, charge transferred per time: I=Q/t A 15 A current that acts for 0.1 s will transfer 15 A × 0.1 s = 1.5 C of charge." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

Ohm's law

V=IR "where V is the voltage drop, I is the current, and R is the magnitude of the resistance, measured in ohms (Ω). Ohm's law is the basic law of electricity because it states that for a given magnitude of resistance, the voltage drop across the resistor will be proportional to the magnitude of the current. Likewise, for a given resistance, the magnitude of the current will be proportional to the magnitude of the emf (voltage) impressed upon the circuit. The equation applies to a single resistor within a circuit, to any part of a circuit, or to an entire circuit (provided one can calculate the equivalent resistance from all of the resistors in the circuit). As current moves through a set of resistors in a circuit, the voltage drops some amount in each resistor; the current (or sum of currents for a divided circuit) is constant. No charge is gained or lost through a resistor; thus, if resistors are connected in series, all of the current must pass through each resistor." Excerpt From: Kaplan Test Prep. "MCAT Physics and Math Review 2021-2022." Apple Books.

dielectrics in isolated capacitors

Voltage decreases, capacitance increases, charge constant