Physics C: E&M · CED Unit 3: Electric Circuits · 16 min read · Updated 2026-05-11
Electric Circuits — AP Physics C: Electricity & Magnetism
AP Physics C: Electricity & Magnetism · CED Unit 3: Electric Circuits · 16 min read
1. EMF, Current, Resistance & Ohm's Law★★☆☆☆⏱ 3 min
All circuits rely on three core quantities, defined below, linked by the empirical Ohm's Law for ohmic materials.
Ohm's Law states that for ohmic materials (constant resistance independent of applied voltage), the potential difference across a resistor is proportional to the current flowing through it:
V = IR
2. Kirchhoff's Circuit Rules★★★☆☆⏱ 4 min
Kirchhoff's two rules, derived from fundamental conservation laws, allow you to solve for unknown currents and voltages in any multi-loop circuit that cannot be reduced to simple series/parallel equivalents.
\sum I_{in} = \sum I_{out}
\sum \Delta V = 0
Assign arbitrary current directions for each branch; a negative final result means current flows opposite your assigned direction.
KVL sign convention: Moving across a resistor in the direction of current: $\Delta V = -IR$; moving opposite current: $\Delta V = +IR$. Moving from negative to positive terminal of a battery: $\Delta V = +\varepsilon$; positive to negative: $\Delta V = -\varepsilon$.
3. Transient Behavior of RC Circuits★★★☆☆⏱ 3 min
RC circuits combine resistors and capacitors, with time-dependent charge and current behavior when connected to or disconnected from a voltage source. For a charging series RC circuit with an initially uncharged capacitor connected to EMF $\varepsilon$ at $t=0$, KVL gives the differential equation:
\varepsilon - IR - \frac{Q}{C} = 0
Substitute $I = \frac{dQ}{dt}$ and integrate from $Q=0$ at $t=0$ to get the exponential charge relation. The time constant for an RC circuit is $\tau = RC$, the time to reach ~63% of maximum charge.
RL circuits combine resistors and inductors, where inductors oppose changes in current via a back EMF $\varepsilon_L = -L\frac{dI}{dt}$, with $L$ the inductance in Henries (H). For a series RL circuit connected to EMF $\varepsilon$ at $t=0$, KVL gives:
\varepsilon - IR - L\frac{dI}{dt} = 0
Integrating from $I=0$ at $t=0$ gives the current relation for a growing current, with time constant $\tau = \frac{L}{R}$.
\text{Decaying current (source removed): } I(t) = I_0 e^{-t/\tau}
Key transient behavior rules for DC circuits:
At $t=0$: Uncharged capacitors act as short circuits (zero resistance), inductors act as open circuits (infinite resistance, zero current)
At $t \to \infty$ (steady state): Capacitors act as open circuits (zero current), inductors act as short circuits (zero voltage drop)
5. Power and Energy in Circuits★★☆☆☆⏱ 2 min
Power is the rate of energy transfer in a circuit, measured in Watts (W). For any circuit component with potential difference $V$ across it and current $I$ through it, general power is:
P = IV
For ohmic resistors, substitute Ohm's Law to get alternative forms for power dissipated as heat via Joule heating:
P = I^2 R = \frac{V^2}{R}
Energy is stored in the electric field of capacitors and magnetic field of inductors, with the following relations: