MCAT Physics - (6) Circuits
Current in Series/Parallel
*Kirschhoff's junction rule*... current in must equal current out. current is constant in series, but different in parallel (Though the current out of the junction equals the current in).
Resistance of Resistors in parallel
1/R (parallel) = 1/R1 + 1/R2 + 1/R3 + 1/Rn
KEY CONCEPT: Dielectric constant
A dielectric material can never decrease the capacitance; thus, K can never be less than 1.
Siemens
A unit of conductance. Siemens/meter = conductance.
Alternating Current
AC, refers to an alternating flow of charge (though only ever in one direction at any given time).
Resultant Resistor
Also known as the equivalent resistor, refers to treating resistors in series with one another as a single large resistor, such that: R1 + R2 + R3 = R4 for example.
Types of Electric Meters
Ammeters: measure the current at some point in the circuit. Voltmeters: measure the voltage at some point in the circuit. Ohmmeters: measure the resistance at some point.
Kirchhoff's Loop Rule
Around any closed circuit loop (which frequently occur with parallel resistors and capacitors), the sum of voltage sources will always be equal to the sum of voltage drops. V (source) = V (drop)
Kirchhoff's Junction Rule
At any junction point in a circuit, the sum of all the currents flowing into the junction must equal to sum of the current exiting the junction. I (in) = I (out).
Useful Equations Associated with Capacitance and Dielectric constants
C = Q/V C' = Q/V' = C = CV/V'
Capacitance of a parallel plate capacitor (equation)
C = ε(naught)(A/d) C =
KEY CONCEPT: Flow of Current and Electrons.
Current, by convention, flows from a higher electric potential to a lower electric potential. In contrast, electrons flow from a lower electronic potential to a higher electronic potential.
Direct Current
DC, refers to a unidirectional flow of charge.
Ohm's Law
Describes the Voltage drop between any two points in a circuit as a function of current and resistance. V = IR Which can be manipulated of course: I = V/R
Uniform electric field between plates of capacitor (equation)
E = V/d
True or False: The sum of the voltage sources in a circuit is equal to the sum of the voltage drops in that circuit.
False. Though this is the case in a closed circuit, it is not necessarily true for the circuit as a hole. For example, a 9 V battery that powers 3 light bulbs in parallel has a 9 V voltage source and a 9 V drop across each light bulb-- a total of 27 V of drop across all of the light bulbs combined. Note that the picture has 3 closed loops, each one containing a light bulb in parallel with another.
Parallel Resistors
For resistors in parallel, the current is spread across the resistors of different junctions, though the voltage is the same through them all (just like with the lightbulb example where the voltage source was 9V across 3 lightbulbs is 27V total drop (9V each)). 1/R (parallel) = 1/R1 + 1/R2 + 1/Rn Current chooses the path of least resistance. (contrary to capacitance series/parallel relationship)
Resistors in Series
For resistors in series, the current has no choice by to travel through each resistor in order to return to the cell (current is constant, but voltage drops as energy is dissipated). R (series) = R1 + R2 + R3 + Rn Where n is the number of the resistor in series. (contrary to capacitance series/parallel relationship)
How does temperature affect resistance of current?
Generally, resistance increases with increasing temperature because there is more movement of particles which prevents the flow of current (kinda like traffic).
Capacitors
Have the ability to store and discharge electrical potential energy. Strength is represented by capacitance. C = Q/V
Equation for the Magnitude of Current
I = Q/Δt Where I is the current in amperes [C/s], Q is the charge [C], and Δt is the change in time [s].
KEY CONCEPT: Kirchhoff's Loop Rule
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 according to conservation of energy.
KEY CONCEPT: Internal Resistance
If the cell is not actually driving any current (such as when a switch is in the open position), then the internal resistance is zero, and the voltage of the cell is equal to its emf. For cases when the current is not zero and the internal resistance is not negligible, then voltage will be less than emf.
Resistance (electrical)
Is the opposition to the flow of charge through a substance. Materials that have virtually no resistance are conductors, whereas those with a lot of resistance are insulators (Somewhere in the middle resistors). Resistance is given in ohms [Ω = R = ρL/A where ρ is the rR = ρL/A where ρ is the resistivity, L is the length, and A is the cross-sectional area.esistivity, L is the length, and A is the cross-sectional area.
What happens when a dielectric material is placed in an isolated charged capacitor and a charged capacitor within a circuit?
Isolated/Charged: Voltage across the capacitor is reduced because the dielectric material will shield the charges from one another, Though the net charge remains the same. Circuit/Charged: Charge on capacitor increases whilst the voltage remains constant (must be the same as the source).
KEY CONCEPT: Effect of insulator in Isolated/Open Capacitor
Isolated: Voltage is reduced while charge remains constant. Open: Charge is increased while voltage remains constant.
Dielectric Constant
K, is the factor by which a conductor's capacitance is changed when a dielectric material (insulator) is placed between its conducting regions. Imaged is the new capacitance, C', after the influence of the dielectric constant on the previous capacitance, C.
Circuit Laws
Kirchhoff's Junction Rule: Any current flowing into a junction must flow out of it. Kirchhoff's Loop Rule: Around any closed loop, the sum of voltage sources will always be equal to the sum of voltage drops.
KEY CONCEPT: Kirchhoff's 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 a junction.
Ammeters
Measure the current at some point in a circuit. They are placed in series with the point of interest and operate best with 0 resistance.
Voltmeters
Measures the potential difference (voltage) at some point in the circuit. They are placed in parallel with the circuit element of interest and operate best with infinite resistance.
Ohmmeter
Measures the resistance at some point in the circuit. They are place at two points in series with the circuit element of interest and operate best with 0 resistance.
Useful Equations Associated with Ohm's Law
Ohm's Law is V = IR Net current through circuit is equal to: I (net) = V (source)/R1 + V (source)/R2 +... OR I (net) = V (source) / R (series / parallel).
Power (definition and relation to electricity)
P = W/t = ΔE/t = IV = I^(2)R = V^(2)/R P = IV = I^(2)R = V^(2)/R Power dissipates by the resistor of an electrical circuit.
Equation of Resistance (electric)
R = ρL/A where ρ is the resistivity, L is the length, and A is the cross-sectional area.
Electrolytic Conductivity
Refers to aqueous solutions being used to conduct current. Electrolytic solutions ability to conduct current largely depends upon what atoms were dissolved into them. NaCl (table salt) makes for a strong electrolytic solutions because of the Na+ and Cl- ions that form. Whereas DI water is not a good conductor (insulator in fact).
Conductance
Refers to how well a substance can conduct energy. Defined as the reciprocal of resistance (1/R). It is given in units of Siemens/meter [S/m].
Metallic Conductivity
Refers to metals being used to conduct current. Metals are good conductors because they have low electronegativies / ionization energies (they do not hold onto electrons, so they can flow easily).
Conductivity (electrical)
Refers to the ability of a substance to allow charge (electrons) to flow through it. Given in units of Conductance [Conductance = S/m], where S is siemens. Divided into two categories: metallic and electrolytic conductors.
Internal Resistance
Refers to the small, but relevant resistance associated with the voltage source of the circuit. The actual voltage supplied by the cell to a circuit is shown to the right. V = E (Cell) - iε (res).
KEY CONCEPT: Voltage drop across resistors in parallel (Kirchhoff's loop rule).
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.
Resistivity (electric)
Represented by ρ, resistivity revers to the intrinsic ability of a material to resist the flow of charge through it. It is given in units of Ω*m [ρ = Ω*m ] Similar to the specific heat of a substance (thermal energy), resistivity is entirely based on the intrinsic ability of the substance
How does cross-sectional area affect resistance of current?
The cross-sectional area of a wire is inversely proportional to the resistance (if the area is halved, then the resistance will be twice as large). Area = πr^(2) will frequently be used to determine the area.
Current
The flow of positive charge (antiparallel to the flow of electrons). Given in units of Ampere [A = C/s] There are two patterns of current flow: direct current (DC) and alternating current (AC).
How does wire length affect resistance of current?
The length of a wire is directly proportional to the resistance felt by the wire (if the wire is 2x as long, the resistance will be twice as large).
MCAT Expertise: Resistors
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 resistors 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.
Capacitance
The ratio of the magnitude of the charge stored in on the plate of a capacitor to the potential difference across it. C = Q/V Given in units of farad [F = C/J]
Capacitors in Parallel
Total Capacitance increases as the voltage through in parallel path is the same, so the cumulative capacitance is greater. C (parallel) = C1 + C2 + Cn (contrary to resistance series/parallel relationship)
Capacitors in Series
Total capacitance decreases as they share the voltage drop in the loop. 1/C(series) = 1/C1 + 1/C2 + 1/Cn (contrary to resistance series/parallel relationship)
Potential Energy of a Capacitor
U=1/2CV^2
Actual Voltage Supplied by a Cell
V = E (cell) - iε (res) where V is the voltage, E (Cell ) is the emf of the cell, i is the current through the cell, and ε (res) is the internal resistance.
Voltage drops across resistors in series
Voltage is dissipated along each resistor. The net voltage drop can be given by: V (series) = V1 + V2 + V3 + Vn Where Vn is the voltage drop across each individual resistor.
Voltage drop across resistors in parallel
Voltage is the same over every junction, but they accumulate at the end of the circuit such that: V (parallel) = V1 + V2 + Vn
KEY CONCEPT: Resistors in Parallel Problems
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).
Electromotive Force
emf, or ε, is the potential difference (voltage) between two terminals of a cell that have no charge flowing between them. Because it is a voltage, its units are [V = J/C]
Permittivity of free space
ε(naught) = 8.85 x 10 ^(-12) F/m