Chapter 4 - Electric Circuits

: the amount of charge passing a point in a given time period**Current**I = ΔQ/Δt

I: current (Amperes)

Q: charge (Coulombs)

t: time (seconds)

Current is described in the AP exam as the flow of positive charge

: create currents using a difference in potential**Batteries**The “+” terminal has a higher electric potential

The “-” terminal has a lower electric potential

Generally, the greater the potential difference, the more current flows

: a property of the circuit that resists the current**Resistance**Units are Ohms (Ω)

R = ⍴L/A

R: resistance

⍴: resistivity

L: length of wire

A: cross-sectional area of wire

Ohm’s Law

I = ΔV/R

ΔV: voltage across a certain part of the circuit (like a resistor)

R: resistance

I: current

Power: the rate at which electrical energy is converted to heat energy

P = IΔV = I^2 R = ΔV^2/R

Ohmic vs. Nonohmic

: a circuit part (resistor or capacitor) that maintains the same resistance when the voltage across it or current through it changes - resistance is constant**Ohmic**

Circuit Pictures

Wire: straight line

Battery: 4 parallel lines - one long line and then one smaller line repeated

Resistor: zig zag line

Capacitor: 2 parallel lines

Resistors in Series

R = ⅀Ri

Ri: the resistances of the resistors in series with each other

R: equivalent resistance or total resistance

Resistors in Parallel

1/R = ⅀1/Ri

Ri: the resistances of the resistors in parallel with each other

R: equivalent resistance or total resistance

Rules for resistors in circuits

The current in resistors in series is equal to each other

The voltage across resistors in parallel is equal to each other

The voltage across two resistors in parallel is also equal to the voltage across each individual resistor

V-I-R charts

Create columns of V, I, and R for each individual resistor and the total circuit

This helps us stay organized in complex problems

: The current entering and leaving a junction is equal**Junction Rule**: In a closed loop, the sum of the voltages is 0**Loop Rule**Choose a loop of the circuit and when you see a resistor, the voltage is -IR because resistors resist the current

If the loop is against the current, the voltage is +IR

When you see a batter, add the voltage of the battery (if going from - to +)

If you go from + to -, subtract the voltage of the battery

If the current you calculate is negative, you chose the wrong direction and the current flows the opposite way

In calculations, we assume most electronic devices in circuits act as resistors

Light bulb

The brightness of a bulb depends only on the power dissipated

The power of a bulb can change depending on the current and voltage of the circuit it’s in

Ammeters and Voltmeters

Ammeters: measure current

Ammeters work by putting them in series with resistors (current is constant for resistors in series)

Voltmeters: measure potential difference (voltage)

Voltmeters work by putting them parallel to parallel resistors

Real batteries

In a perfect world, batteries have no resistance but in the real world, this is not true

The voltage advertised by a battery, ε, is actually larger than the real voltage ΔV (terminal voltage)

ΔV = ε - Ir

r: the internal resistance of the battery

I: current through the battery

Internal resistance is measured by hooking a battery up to a resistor and plotting the terminal voltage of the battery as a function of the current through the battery

The slope will be equal to -r

Switches

Open switch: that part (loop) of the circuit can be considered gone (dead)

Capacitors

: two parallel metal plates separated by either air or dielectric material**Capacitors**Capacitance: how much charge a capacitor can hold for each volt of potential difference

C = kεA/d

C: capacitance

k: dielectric constant

ε: vacuum permittivity constant

A: area of one of the plates (both plates have the same area)

d: distance between plates

ΔV = Q/C

ΔV: Voltage

Q: charge

C: capacitance (Farads)

U = 1/2 QΔV = 1/2 C(ΔV )^2

U: energy stored in a capacitor

Q: charge

ΔV: potential difference

C: capacitance

ΔV/Δr = E

E: electric field

ΔV: potential difference

Δr: distance between plates

Parallel vs. Series Capacitors

Parallel Capacitors

C = ⅀Ci

C: total capacitance for capacitors in parallel

Ci: capacitance of capacitors in parallel

This is the same formula from resistors in series - capacitors are basically resistors in reverse

Series Capacitors

1/C = ⅀1/Ci

C: total capacitance for capacitors in series

Ci: capacitance of capacitors in series

: a circuit containing resistor(s) and capacitor(s)**RC Circuit**You’ll only be asked about RC Circuits in certain states

When you first connect a capacitor to a circuit:

No charge has built up so treat the capacitor like a wire with no potential difference

After a long time:

The capacitor has charged up to its max so no current will flow through it

Treat the capacitor like an open switch

The potential difference across the capacitor equals the voltage of the devices parallel to the capacitor

: the amount of charge passing a point in a given time period**Current**I = ΔQ/Δt

I: current (Amperes)

Q: charge (Coulombs)

t: time (seconds)

Current is described in the AP exam as the flow of positive charge

: create currents using a difference in potential**Batteries**The “+” terminal has a higher electric potential

The “-” terminal has a lower electric potential

Generally, the greater the potential difference, the more current flows

: a property of the circuit that resists the current**Resistance**Units are Ohms (Ω)

R = ⍴L/A

R: resistance

⍴: resistivity

L: length of wire

A: cross-sectional area of wire

Ohm’s Law

I = ΔV/R

ΔV: voltage across a certain part of the circuit (like a resistor)

R: resistance

I: current

Power: the rate at which electrical energy is converted to heat energy

P = IΔV = I^2 R = ΔV^2/R

Ohmic vs. Nonohmic

: a circuit part (resistor or capacitor) that maintains the same resistance when the voltage across it or current through it changes - resistance is constant**Ohmic**

Circuit Pictures

Wire: straight line

Battery: 4 parallel lines - one long line and then one smaller line repeated

Resistor: zig zag line

Capacitor: 2 parallel lines

Resistors in Series

R = ⅀Ri

Ri: the resistances of the resistors in series with each other

R: equivalent resistance or total resistance

Resistors in Parallel

1/R = ⅀1/Ri

Ri: the resistances of the resistors in parallel with each other

R: equivalent resistance or total resistance

Rules for resistors in circuits

The current in resistors in series is equal to each other

The voltage across resistors in parallel is equal to each other

The voltage across two resistors in parallel is also equal to the voltage across each individual resistor

V-I-R charts

Create columns of V, I, and R for each individual resistor and the total circuit

This helps us stay organized in complex problems

: The current entering and leaving a junction is equal**Junction Rule**: In a closed loop, the sum of the voltages is 0**Loop Rule**Choose a loop of the circuit and when you see a resistor, the voltage is -IR because resistors resist the current

If the loop is against the current, the voltage is +IR

When you see a batter, add the voltage of the battery (if going from - to +)

If you go from + to -, subtract the voltage of the battery

If the current you calculate is negative, you chose the wrong direction and the current flows the opposite way

In calculations, we assume most electronic devices in circuits act as resistors

Light bulb

The brightness of a bulb depends only on the power dissipated

The power of a bulb can change depending on the current and voltage of the circuit it’s in

Ammeters and Voltmeters

Ammeters: measure current

Ammeters work by putting them in series with resistors (current is constant for resistors in series)

Voltmeters: measure potential difference (voltage)

Voltmeters work by putting them parallel to parallel resistors

Real batteries

In a perfect world, batteries have no resistance but in the real world, this is not true

The voltage advertised by a battery, ε, is actually larger than the real voltage ΔV (terminal voltage)

ΔV = ε - Ir

r: the internal resistance of the battery

I: current through the battery

Internal resistance is measured by hooking a battery up to a resistor and plotting the terminal voltage of the battery as a function of the current through the battery

The slope will be equal to -r

Switches

Open switch: that part (loop) of the circuit can be considered gone (dead)

Capacitors

: two parallel metal plates separated by either air or dielectric material**Capacitors**Capacitance: how much charge a capacitor can hold for each volt of potential difference

C = kεA/d

C: capacitance

k: dielectric constant

ε: vacuum permittivity constant

A: area of one of the plates (both plates have the same area)

d: distance between plates

ΔV = Q/C

ΔV: Voltage

Q: charge

C: capacitance (Farads)

U = 1/2 QΔV = 1/2 C(ΔV )^2

U: energy stored in a capacitor

Q: charge

ΔV: potential difference

C: capacitance

ΔV/Δr = E

E: electric field

ΔV: potential difference

Δr: distance between plates

Parallel vs. Series Capacitors

Parallel Capacitors

C = ⅀Ci

C: total capacitance for capacitors in parallel

Ci: capacitance of capacitors in parallel

This is the same formula from resistors in series - capacitors are basically resistors in reverse

Series Capacitors

1/C = ⅀1/Ci

C: total capacitance for capacitors in series

Ci: capacitance of capacitors in series

: a circuit containing resistor(s) and capacitor(s)**RC Circuit**You’ll only be asked about RC Circuits in certain states

When you first connect a capacitor to a circuit:

No charge has built up so treat the capacitor like a wire with no potential difference

After a long time:

The capacitor has charged up to its max so no current will flow through it

Treat the capacitor like an open switch

The potential difference across the capacitor equals the voltage of the devices parallel to the capacitor