Electric Circuits: every key term you need (+ practice quiz)

More AP Physics C: E&M guides

• Conductors, Capacitors, and Dielectrics
• Magnetic Fields and Forces
• Electromagnetic Induction and Maxwell's Equations

Electric Current

Rate of charge flow, I = dQ/dt, measured in amperes (1 A = 1 C/s); conventional current points in the direction positive charge would move.

Current Density

J = I/A, current per unit cross-sectional area; microscopically J = nqv_d relates it to carrier density and drift velocity.

Drift Velocity

Average velocity of charge carriers superimposed on their random thermal motion — typically only millimeters per second in household wires.

Ohm's Law

V = IR for ohmic materials: current is proportional to applied voltage, with resistance R independent of V.

Resistance

R = ρL/A: resistance grows with length, shrinks with cross-sectional area, and scales with the material's resistivity.

Resistivity

ρ, an intrinsic material property (Ω·m); metals have low ρ that rises with temperature as lattice vibrations scatter electrons more.

Microscopic Ohm's Law

J = σE (σ = 1/ρ is conductivity): the local current density is proportional to the local field driving the carriers.

Electric Power

P = IV = I²R = V²/R; the rate electrical energy is converted to heat, light, or mechanical work in a circuit element.

Joule Heating

Energy dissipated in a resistor as carriers collide with the lattice; a resistor carrying current I dissipates I²R watts as heat.

EMF (Electromotive Force)

Energy per unit charge a source (battery, generator) delivers, ε in volts; it is work per charge, not actually a force.

Internal Resistance

Real batteries behave as ideal EMF ε in series with resistance r; terminal voltage V = ε − Ir droops as current increases.

Terminal Voltage

The actual potential difference across a battery's terminals: less than ε when discharging, greater than ε when being charged.

Kirchhoff's Junction Rule

Sum of currents into a node equals sum out — conservation of charge applied to circuit junctions.

Kirchhoff's Loop Rule

The sum of potential changes around any closed loop is zero — conservation of energy for circuit charges.

Resistors in Series

Same current through each; voltages add, so R_eq = R₁ + R₂ + … is larger than any individual resistance.

Resistors in Parallel

Same voltage across each; currents add, so 1/R_eq = 1/R₁ + 1/R₂ + … is smaller than the smallest branch.

Voltage Divider

Two series resistors split the source voltage in proportion to resistance: V₁ = ε·R₁/(R₁+R₂).

Ammeter

Measures current; connected in series with the element, and ideally has zero resistance so it does not alter the current.

Voltmeter

Measures potential difference; connected in parallel across the element, and ideally has infinite resistance so it draws no current.

RC Circuit (Charging)

A capacitor charging through a resistor follows q(t) = Cε(1 − e^(−t/RC)); current starts at ε/R and decays exponentially.

RC Circuit (Discharging)

A charged capacitor discharging through R follows q(t) = Q₀e^(−t/RC), with current and voltage decaying with the same time constant.

Time Constant τ = RC

Characteristic time of an RC circuit; after one τ, a charging capacitor reaches 63% of its final charge, and a discharging one falls to 37%.

Capacitor at t = 0

An uncharged capacitor momentarily acts like a wire (no voltage across it), so initial currents are found by short-circuiting it.

Capacitor at Steady State

Fully charged, a capacitor passes no current and acts like an open switch; steady-state currents are found by removing it from the circuit.

Deriving RC Behavior

Apply the loop rule ε − iR − q/C = 0 with i = dq/dt, separate variables, and integrate — the exponential solutions follow from this ODE.

Power Delivered by EMF

P = εI is the total power a source supplies; it splits between internal dissipation I²r and power to the external circuit.

Maximum Power Transfer

External load receives maximum power when R_load equals the source's internal resistance r; then P_load = ε²/(4r).

Superconductor

Material whose resistivity drops to exactly zero below a critical temperature, allowing persistent currents without dissipation.

Non-Ohmic Devices

Elements like diodes and filament bulbs whose I–V curves are not straight lines; R = V/I still applies pointwise but is not constant.

Wire Gauge Intuition

Thick wires (large A) have low resistance; a wire stretched to double length at constant volume quadruples its resistance (L doubles, A halves).

Multiloop Analysis

Assign branch currents, write junction equations and independent loop equations, and solve the linear system; a negative answer means the assumed direction was reversed.

Energy in RC Charging

Charging a capacitor through a resistor to charge Q wastes exactly half the battery's energy: the battery supplies QV, the capacitor stores ½QV, and I²R heat takes the rest.

Ideal vs Real Battery Check

If shorted, a real battery delivers I = ε/r, not infinite current; terminal voltage collapses to zero across the short.

Household Wiring

Outlets are wired in parallel so each appliance sees the full line voltage and can operate independently; a blown branch does not kill the others.