AP Physics C: E&M — Unit 3: Electric Circuits

Electric Current

The rate at which charge passes through a given cross-sectional area.

Average Current Formula

I = ΔQ/Δt

Calculus Definition of Current

I = dQ/dt

Unit of Current

Ampere (A), where 1 A = 1 C/s.

Conventional Current Direction

The direction in which positive charge would move, from high to low potential.

Current Density (J)

The current per unit area.

Current Density Formula

I = nqAvd, where n is charge carrier density, q is charge, A is area, and vd is drift velocity.

Drift Velocity

The average slow velocity of electrons moving against the electric field due to collisions.

Resistance (R)

The opposition to current flow.

Resistivity (ρ)

An intrinsic property of the material, independent of its shape.

Resistance Formula (Geometry)

R = ρ(L/A), where L is length and A is cross-sectional area.

Temperature Dependence of Resistivity

Resistivity typically increases with temperature for metals.

Ohm's Law (Macroscopic Form)

V = IR, illustrating the relationship between Voltage, Current, and Resistance.

Microscopic Form of Ohm's Law

E = ρJ or J = σE, where σ is conductivity.

Electromotive Force (EMF)

The work done per unit charge to move charge from low to high potential inside the source.

Terminal Voltage (V_term) Formula

V_term = EMF - Ir, where r is the internal resistance.

Electric Power (P)

The rate at which electrical potential energy is converted into other forms.

General Formula for Electric Power

P = IV = dW/dt.

Kirchhoff's Junction Rule

The sum of currents entering any junction must equal the sum of currents leaving it.

Kirchhoff's Loop Rule

The algebraic sum of potential differences around any closed circuit loop must be zero.

Voltage for Resistors in Series

The total voltage is the sum of the voltages across each resistor.

Current for Resistors in Series

The same current flows through each resistor.

Equivalent Resistance for Resistors in Series

Req = ΣRi.

Voltage for Resistors in Parallel

Same voltage across each resistor.

Current for Resistors in Parallel

The total current is the sum of the currents through each resistor.

Equivalent Resistance for Resistors in Parallel

1/Req = Σ(1/Ri).

Ammeter

A device that measures current, connected in series with ideal resistance of 0 Ω.

Voltmeter

A device that measures potential difference, connected in parallel with ideal resistance of infinite Ω.

Capacitance in Series

1/Ceq = Σ(1/Ci), lowers capacitance.

Capacitance in Parallel

Ceq = ΣCi, increases capacitance.

Potential Energy in Capacitors

U_C = 1/2 QV = 1/2 CV^2 = 1/2 (Q^2/C).

Time Constant (τ)

τ = RC, indicating the response time of an RC circuit.

Charging a Capacitor Initial State

At t=0, the capacitor is a short circuit and current is maximum.

Charging a Capacitor Steady State

At t approaches infinity, the capacitor is fully charged and acts as an open circuit.

Charge during Charging Phase

q(t) = CEMF(1 - e^(-t/RC)).

Current during Charging Phase

I(t) = (EMF/R)e^(-t/RC).

Voltage across Capacitor during Charging Phase

V_c(t) = EMF(1 - e^(-t/RC)).

Discharging a Capacitor

Charge decreases over time according to q(t) = Q_0 e^(-t/RC).

Current during Discharging Phase

I(t) = - (Q_0/RC)e^(-t/RC) (negative indicates direction).

Voltage across Capacitor during Discharging Phase

Vc(t) = V0 e^(-t/RC).

Common Mistake 1

Confusing steady-state vs. transient states in circuits.

Common Mistake 2

Incorrect hookup of ammeters and voltmeters.

Common Mistake 3

Confusing power with energy.

Common Mistake 4

Misinterpreting brightness of bulbs in terms of power.

Common Mistake 5

Confusing local vs global resistance in calculations.