TPR Chapter 10: Electricity and magnetism.

Effect of a dielectric on property of capacitor: If a charge capacitor with a dielectric is disconnected from battery source, how does this affect the capacitance, charge, voltage and electric field? If a charge capacitor with a dielectric is still connected to the battery source, how does this affect the capacitance, charge, voltage and electric field?

#1. Disconnecting battery from charged capacitor and inserting dielectric results in an increased capacitance, same charge and decreased voltage and electric field by factor of K. #2. Inserting dielectric with voltage connected capacitor results in an increased charge and capacitance by factor of K. Voltage and electric field stays the same.

Right hand rule

+ sign = into the page, away from you (Think of the butt of an arrow moving away from you). o sign = out of the page, towards you. (think of the head of the arrow coming towards you). Thumb: direction of the force (F). Index finger: direction of velocity (v) of moving charge. Middle finger: direction of magnetic field (B). 1: point index finger in the direction of the moving charge. 2. then point middle finger towards or away from self. 3. This will give the direction of the thumb.

Ammeter

- A device used to measure current in a circuit. - Must be connected in series to the resistor or battery. - Has low internal resistance.

Voltmeter

- A device used to measure voltage in a circuit or battery. - Must be connected in parallel to the resistor. - Has a high internal resistance.

Can a magnetic force change speed of a particle? Does magnetic force do work? Describes the motion of a charged particle in a uniform magnetic field in a direction perpendicular to that field?

- No. A magnetic force cannot change the speed of a charge particle, only its direction. - Therefore magnetic force does not do work. - When a charged particle enters a uniform magnetic field in a direction perpendicular to that field, its motion is continuously changed by the magnetic force. It ends up moving in a circle with a radius.

What is the purpose of capacitor?

1. Create a uniform field; always point from positive plate to negative plate; 2. store electrical potential energy.

Kirchhoff's Laws

1. The sum of current flowing into a junction must equal the sum of the current leaving at any junction. 2. The sum of voltage sources = the sum of voltage drops around a closed-circuit loop

Centripetal force definition. What is the direction of the force? Where does it point to?

Any net force causing uniform circular motion. The direction of a centripetal force is always perpendicular to path of motion and points towards the center of curvature, the same as the direction of centripetal acceleration.

Magnitude of magnetic field on a current carrying wire

B = (current/radius). magnitude of the magnetic field increases with current and decreases with distance.

Tesla units

B = F/(qv sinθ). = N/(C · m/s) = 1 T

Capacitance of parallel plate capacitor. Unit of capacitance. is capacitance dependent on charge and voltage?

C = ϵ* (A/d). unit: C/V = Farad. ϵ = permittivity of free space. Capacitance only depends on area and distance and not charge or voltage.

Parallel circuit: - Description of setup. - How many path does current has to flow? - The current is ------ through each resistor. - The voltage is ------- through each resistor. - How to calculate equivalent resistance? - The equivalent resistance is (greater or smaller?) than the largest resistor. - What does adding more resistor in a series circuit do to current?

A circuit that contains more than one path for current flow. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total:equivalent resistance of resistors in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +... The equivalent resistance is smaller than the largest resistor. In parallel circuit adding more resistors decreases total resistance and thus increases current. This is because adding more resistors creates more choices for current to flow.

Capacitors diagram - Definition. - What is the total net charge on a capacitor? - What develops between the metal conductors?

A device used to store an electric charge, consisting of two pieces of metal conductors carrying equal but opposite charge, separated by an insulator. Net charge is 0 because capacitor consists of two oppositely charged plates of equal magnitude. An electric potential difference V develops between the conductors. Charges stop flowing when potential difference between the parallel plate matches the voltage battery because at this point, the circuit will look like one that has two opposing voltage source. Electrical potential energy is stored in a uniform electric field, generated by the charge distribution on the two plates.

ferromagnetic material

A material that is strongly attracted to a magnet, and which can be made into a magnet.

Series circuit: - Description of setup. - How many path does current has to flow? - The current is ------ through each resistor. - How to calculate equivalent resistance? - The equivalent resistance is (greater or smaller?) than the largest resistor. - What does adding more resistor in a series circuit do to current? - What is the main disadvantage in series circuit?

A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: equivalent resistance of resistors in series : R = R1 + R2 + R3 + ... The equivalent resistance is greater than the largest resistor. In a series circuit, adding more resistors increases total resistance and thus lowers current. The main disadvantage of a series circuit is that if there is a break in the circuit the entire circuit is open and no current will flow. If a light bulb on a Christmas tree string goes out, all the other bulbs will stop working.

Series circuit problem. If the values of the three resistors are: R1 = 8 Ω, R2 = 8 Ω, & R3 = 4 Ω with a 10 V. Calculate the total resistance and current.

A series circuit is shown in the diagram above. The current flows through each resistor in turn. If the values of the three resistors are: R1 = 8 Ω, R2 = 8 Ω, & R3 = 4 Ω Total resistance R = R1 + R2 + R3 = 8 Ω,+ 8 Ω, +4 Ω = 20 Ω With a 10 V battery, by V = I R the total current in the circuit is: I = V / R = 10 / 20 = 0.5 A. The current through each resistor would be 0.5 A.

What happens to the current in other bulbs if one bulb in a series circuit burns out?

All bulbs will go out and the the current will be zero.

Magnets

Always dipole. Not monopole.

Dielectric

An electrical insulator that keeps parallel plates from touching each other. Increases capacitance, therefore ability to store energy.

DC circuits: - What is the conventional flow of current? - What is the direction of electric charge in relation to electrical potential?

Direct Current (DC) is the constant flow of electric charge from high to low potential. Conventional current is defined as a flow of positive charge from high potential (+ terminal) to low potential (- terminal)

Electric field in a capacitor equation.

E = V/d.

Centripetal force and acceleration equation. How does increasing the centripetal force affect the radius of curvature?

F = mv^2/ r. r = mv^2/F. This implies that for a given mass and velocity, a large centripetal force cause a small radius of curvature.

Magnetic force on a wire carrying current equation

F = qvB F = (C) x (m/s) x (T). rearrange to include current and length: F = (C/s) x (m) x (T) F= I x L x B

Magnetic force equation: - Provide equation. - Magnetic force is ------- to plane formed by the ------ and -------. - Magnetic force is 0 if V and B are ------. Results in charge particle following magnetic field lines rather than crossing them. - Any charge moving --- or anti --- to the direction of the magnetic field will experience ----- from the magnetic field.

F = q·v·B·sinθ. q = the charge (C). v = velocity (m/s). B = magnetic field strength (T). θ = angle between vector qv and magnetic field B. The force is perpendicular to the plane formed by v and B. Since the force is zero if v is parallel to B, charged particles often follow magnetic field lines rather than cross them. Any charge moving // or anti// to the direction of the magnetic field will experience no force from the magnetic field because: θ = 0; Sin 0 = 0

Within a metal, 5 x 10^17 conducting electrons drift pass a point at 4 seconds, what is the magnitude of the charge?

I = Q/t. Q = (5 x 10^17)(1.6 x 10^19 C) = 8 x 10^-2 C. I = (8 x 10^-2 C)/(4 seconds) = 0.02 A.

Current equation

I = Q/t. Units: C/t

What happens to the current in other bulbs if one bulb in a parallel circuit burns out?

If one lamp in a parallel circuit burns out, the other lamps are unaffected because current still flows through them. Total current in the system is reduced by the loss of the burned out lamp

Equivalent resistance of resistors in parallel

If only two resistors, use this equation: Req = R1R2/R1+R2.

Resistors connected in parallel problem: If the values of the three resistors are: R1 = 8 Ω, R2 = 8 Ω, & R3 = 4 Ω, with a voltage of 10 V. calculate the total resistance and current.

In the diagram, the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance. If the values of the three resistors are: R1 = 8 Ω, R2 = 8 Ω, & R3 = 4 Ω. total eq resistance 1 / R = 1 / R1 + 1 / R2 + 1 / R3 + = (1/8 + 1/8 + 1/4) = 1/2. 1/R = 1/2; R = 2. With a 10 V battery, by V = I R the total current in the circuit is: I = V / R = 10 / 2 = 5 A. The individual currents can also be found using I = V / R. The voltage across each resistor is 10 V, so: I1 = 10 / 8 = 1.25 A I2 = 10 / 8 = 1.25 A I3=10 / 4 = 2.5 A.

What is the resulting path of a moving charge in a uniform magnetic field?

In uniform circular motion, the centripetal force is always perpendicular to direction of the particle's velocity and speed is always constant. All that is changing is the direction. F(B) = F(C) --> qvB = mv^2/(r). r = mv/qB.

Magnetic field: ---------------------------------------------------------------------- - Magnetic fields are created by -------- electrical charges. - If a charged particle is at rest, then an ----- is produced in the surrounding region. - If the charged particle is in motion, then a -------- is produced. - A magnetic field can only exert a force on a charge that is ---- through the field.

Magnetic fields are created by moving electrical charges. If a charged particle is at rest, then an electrical field is produced in the surrounding region. If the charged particle is in motion, then a magnetic field is produced. A magnetic field can only exert a force on a charge that is moving through the field.

What happens to the brightness of each bulb in a parallel circuit if more bulbs are added (in parallel) to the circuit?

Nothing happens to the brightness of the light bulbs in the parallel circuit if the power supply is capable of supplying the required current.

Power equation

P = IV. P = I^2*R. P = V^2/R. P = E/t = W/t.

Which type of circuit has brighter bulbs?

Parallel

Which type of circuit requires the most current flow through the battery?

Parallel

Equations for calculating electric field (for point charges, and capacitors).

Point charge: E = F/q = KQ/r^2. Capacitors: E = V/d. The electric field is reduced in a parallel plate capacitor with a dielectric material because the dielectric material is polarized, producing an oppositing field.

Charge on a capacitor equation: Units of capacitance? Is capacitance dependent on charge and voltage?

Q = CV. Q = charge in coulombs. V = voltage (V). C = capacitance proportionality constant. Capacitance is not dependent on charge or voltage. Here is behaves as a constant.

Resistance equation: - Equation containing resistivity. - Equation containing voltage. - Equation containing power. - Equation for fluid.

R = (ρL/A) = (resistivity * Length of wire)/(area of wire). R (fluid): (8* η*L)/(πr^4). R = V/I R = Power/current squared = P/I^2

How much work is done by a moving charge in a magnetic field.

Recall that centripetal forces do no do any work. Work done on the particle should change its kinetic energy. However because the particle is not changing its speed, the kinetic energy does not change. W = Δ KE = 0. Therefore, magnetic field do not do work, because magnetic force only changes direction, not speed. NOTE: uniform electric field CAN change the speed and kinetic energy of charged particles.

Equivalent resistance of resistors in series

Req = R1 + R2 + R3

Capacitors in series and parallel

Series: total equivalent capacitance decreases. Parallel: total equivalent capacitance increases.

What happens to the brightness of each bulb in a series circuit if more bulbs are added (in series) to the circuit?

They get dimmer, since it is a series circuit, all bulbs are exposed to the same current, and every bulb adds resistance (measured in ohms) reducing the amount of energy each bulb has (measured in amperes) since the bulbs have less energy to use, they give off less energy, resulting in a weaker light.

Equation for calculating electrical potential in a capacitor

U = 1/2QV. U = 1/2 CV^2. U = Q^2/2C.

Ohm's Law equation

V=IR.

AC circuit

Voltage and current oscillate in sine wave pattern. Electrical current reverses direction periodically.

What does a voltage create? What is the purpose of a battery?

Voltage creates current because a voltage difference causes electric charges to flow. Battery is use to maintain a constant voltage between terminals.

AC Voltage equation

Vrms = Vmax/√ 2. = Vo/√ 2. Irms = Irms/√ 2 = I/√ 2.

Current and voltage in a parallel circuit.

current: different for each, add to total current across parallel combination. voltage: same for each, equal to total voltage across parallel combination.

Current and voltage in a series circuit.

current: same for all of them, equal to total current through series combination. voltage: different for each but adds to the total voltage across series combination.

Ohm's Law definition

the current in a circuit equals the voltage difference divided by the resistance.

Current definition

the flow of charge per time.

Power

the rate at which work is done