## I. 8.1: ELECTRIC CIRCUITS

### A. CURRENT

1. Current – movement of charge

a) Conduction electrons in a wire are moving all over the place, but there is no net movement of charge (i.e., there is no current)

b) **Drift velocity (v _{d})** – the drift in electron position if there is a current present

2. Current: I = Q/t → unit is Amp (A), or C/s

a) 0.2 A will kill you!

### B. VOLTAGE

This is what causes current (sometimes called electromotor force

### C. RESISTANCE

1. R = V/I → unit is ohm (Ω = V/A)

a) For fixed voltage, note that resistance and current are inversely proportional

2. R = ρL/A

a) ρ is resistivity and is inherent to the material

b) Resistance depends on how we shape the material – a longer, thinner wire has more resistance than a short, fat wire.

3. **OHM’S LAW**

a) V = IR

b) This is more of a statement about the behavior of certain conductors; a material is said to behave Ohm’s law if its resistance, R, remains constant as the voltage is varied; also, the current must reverse directions if the current is reversed

4. ** RESISTORS**

a) Resistors – components with known resistance

b) **RESISTORS IN SERIES** – calculate one “equivalent resistor” by adding up all resistors

(1) **R _{eq} = R_{1} + R_{2} …**

(2) *R _{tot}* will always be larger than the largest resistor!

(3) V_{tot} = V_{R1} + V_{R2} + …. ΣV_{each} = V_{sys}

(4) I_{tot} = I_{R1} = I_{R2} = ….

c) **RESISTORS IN PARALLEL** – More complicated; it is the product of the resistors divided by the sum

(1) **R _{eq} = (R_{1}R_{2})/(R_{1} + R_{2})** → can only use for 2 resistors

(2) **1/R _{eq} = 1/R_{1} + 1/R_{2} + ….**

(3) *R _{tot}* will always be smaller than the smallest resistor!

(4) V_{tot} = V_{R1} = V_{R2} = ….

(5) I_{tot} = I_{R1} + I_{R2} + ….

5. **Kirchoff’s rules**:

a) The Σ of the voltage drops across the resistors in any series = V of the battery

b) The Σ of the current passing through individual resistors in parallel = the current entering the combination

### D. DC CIRCUITS

1. Consists of a voltage source, connecting wire, resistor

2. Note that the direction of the conventional current is opposite the flow of electrons!

3. Working backwards:

a) Series resistors → all resistors share the same current

b) Parallel resistors → all resistors share the same voltage

### E. POWER

1. Power dissipated by resistor: Joule Heating Law

a) **P = I ^{2}R** → in watts (J/s)

2. Power supplied by voltage source:

a) P = IV → in watts (J/s)

(1) V = IR, so P = IIR = I^{2}R

(2) Can use P = IV to calculate power dissipated by resistor, but use for only 1 resistor at a time (best to use P = I^{2}R if calculating power for entire circuit)

3. Power follows law of conservation of energy → power dissipated = power supplied!

## II. 8.2: CAPACITORS

### A. CAPACITOR

A pair of conductors that hold equal but opposite charges; parallel plate capacitor is most common (capacitance is determined by size of plates and distance of plates)

1. Charge on a capacitor occurs because current flows from battery source to the opposing sides of the capacitor

a) Q = CV → Q is the charge on the capacitor, C is constant (capacitance)

(1) Unit is a farad (F) = C/V

2. Capacitance is how much charge can be stored at a certain voltage

a) **C = ε _{0}A/d** → ε

_{0}is constant

b) Note that capacitance is directly related to area, inversely related to distance (the closer the plates are, the greater the force between them and therefore more charge can be stored

3. Electric fields in capacitors: very straightforward

a) **V = Ed** → strength of E depends on voltage and distance between plates

(1) Units are either N/C or V/m → the same thing

4. Electric potential energy stored in capacitors → PE depends of voltage between plates

a) **PE = ½QV** → Q = CV, rewrite to PE = ½CV^{2} = ½Q^{2}/(2C)

5. Discharging capacitor

a) Capacitors discharge on their own, nonlinear (most happens at beginning)

### B. DIELECTRICS

1. **Dielectric** – insulating slab between plates of a capacitor → dielectrics increases capacitance!

2. ** Dielectric constant (K)** – factor that capacitance is multiplied by if dielectric is present

3. Capacitance with dielectric

a) **C = Kε _{0}A/d** → when dielectric is present (K for air ≈ 1)

(1) K tells how much the dielectric increases capacitance

4. Effects of Dielectric on C, V, Q, E, PEE

a) **Disconnecting battery**:

(1) C↑ (by K) according to equation

(2) Q remains the same, since the charges on the capacitor still can’t go anywhere

(3) V↓ (by K) because Q = CV (Q same, C↑ by K, ∴ V↓ by K)

(4) E ↓ (by K) because V = Ed (V↓ by K and d same, ∴ E↓ by K)

(5) PE_{E} ↓ (by K) because PE_{E} = ½QV (Q same, V↓ by K, ∴ PE_{E}↓ by K)

b) **Keeping battery**:

(1) C↑ (by K) according to equation

(2) Q↑ (by K) because Q = CV (C↑ by K and V same, ∴ Q↑ by K)

(3) V remains the same because the capacitor plate voltage will equal the battery voltage

(4) E remains same because V = Ed (V same and d same, ∴ E same)

(5) PE_{E}↑ (by K) because PE_{E} = ½QV (Q ↑ by K, V same, ∴ PE_{E}↑ by K)

### C. DIELECTRIC BREAKDOWN

1. Electrons can jump the space between capacitor plate only under extreme circumstances

a) Each dielectric has a maximum electric field strength where it will no longer act as an insulator

b) **Dielectric breakdown** – when the dielectric is ionized and electrons from capacitor travel across (max electric field strength has been exceeded per distance)

### D. COMBINATION CAPACITORS

1. Capacitors in parallel (like resistor in series)

a) C_{eq} = C_{1} + C_{2} + ….

b) V_{tot} = V_{1} = V_{2} = …..

2. Capacitors in series (like resistors in parallel)

a) 1/C_{eq} = 1/C_{1} + 1/C_{2} + ….. (or product/sum for 2)

b) V_{tot} = V_{1} + V_{2} + ….

## III. 8.3: ALTERNATING CURRENT

### A. Sinusoidal voltage

Voltage goes from peak high to zero to peak low in sinusoidal motion, at a frequency of 60 Hz (60 cycles/sec)

### B. When voltage is > 0, current is going 1 direction and when voltage < 0, current is going the opposite direction

### C. Ohm’s law:

1. v = iR_{eq} → R_{eq} is the equivalent resistance of the circuit

2. Since v and i are changing in AC circuits, we refer to the average v and i (rms)

a) **V _{rms} = V_{max}/√2**

b) **I _{rms} = I_{max}/√2**

3. Other equations are essentially the same:

a) P = I_{rms}^{2}R = I_{rms}V_{rms}

## IV. 8.4: MAGNETIC FIELDS AND FORCES

### A. Electric fields are created by electric charges, magnetic fields are created by moving electric charges

1. Since charge in motion constitutes a current, we can also say that magnetic fields are produced by electric currents

2. Magnetic fields can only exert a force on a charge that is moving through the field

### B. Magnetic force (F_{B})

1. **F _{B} = q(v*B)** → v = velocity of charge q, B = magnetic field

### C. Magnitude of magnetic force

1. **F _{B} = |q|vBsinθ** → θ is the angle between v and B

2. B → magnetic field strength = N/(A∙m) = tesla (T)

### D. Direction of F_{B}

1. Depends on sign of charge

2. Always 丄 to both v and B

3. Right and left hand rules

### E. Work?

No, because the force a charge feels is always 丄 to velocity and charge

1. Magnetic forces can only change direction of a particle, not speed it up or slow it down

2. Most often on MCATs, magnetic force provides centripetal force:

a) F_{c} = mv^{2}/r

b) F_{B} = qvB

c) ∴ **mv/r = qB**

### F. SOURCES OF MAGNETIC FIELDS

1. Since moving charged particles create a magnetic field, a wire with a current will create one

2. A loop of wire will create a magnetic field in the center of the loop

3. **Solenoid** – a coil of wire with a current running through it, creating a magnetic field through the center

### G. MAGNETS

1. Bar magnets create a magnetic field that resembles a magnetic field produced by a circular loop of current-carrying wire

a) Magnetic field lines emanate from north pole, curve around to south pole

b) Electrons of the magnet atoms spin in one direction

## CHAPTER 8 SUMMARY

- Circuits
- Current
- I = Q/t
- In the direction of “flow positive charge”
- Actual flow of electrons is in the opposite direction

- Resistance
- R = ρL/A (ρ = resistivity, not density)

- Ohm’s law:
- V = IR

- Resistors in series:
- R
_{eq}= R_{1}+ R_{2}+ …

- R
- Resistors in parallel:
- 1/R
_{eq}= 1/R_{1}+ 1/R_{2}+ … or R_{eq}= R_{1}R_{2}/(R_{1}+ R_{2}) - Current is the same for resistors in series; voltage is the same for resistors in parallel

- 1/R
- Kirchoff’s Rules:
- The sum of the voltage-drops across the resistors in any complete path is equal to the voltage of the battery
- The amount of current entering a parallel combination of resistors is equal to the sum of the currents that pass through the individual resistors

- Power of circuit element:
- P = IV = I
^{2}R = V^{2}/R

- P = IV = I
- Total power supplied by a battery equals the total power dissipated by the resistors
- The ground is at potential zero
- RMS quantities for AC circuit:
- V
_{rms}= V_{max}/ - I
_{rms}= I_{max}/

- V
- Average power of a circuit element in AC circuit:
- FINISH!!

- I = Q/t

- Current