Physics 2 · Electric Circuits · 16 min read · Updated 2026-05-11
Electric Circuits — AP Physics 2
AP Physics 2 · Electric Circuits · 16 min read
1. Core Quantities and Ohm's Law★★☆☆☆⏱ 3 min
All circuit analysis is built on three core measurable quantities, related by Ohm's law for ohmic materials.
Ohm's law describes the linear relationship between the three quantities for ohmic materials (constant resistance at fixed temperature):
V = IR
2. Kirchhoff's Conservation Laws★★★☆☆⏱ 3 min
For complex multi-loop circuits that cannot be simplified with series/parallel combination rules, use Kirchhoff's two laws, derived from fundamental conservation principles.
To avoid sign errors with KVL, use these consistent conventions when traversing a loop:
Add emf ($+\varepsilon$) when moving from negative to positive battery terminal
Subtract emf ($-\varepsilon$) when moving from positive to negative battery terminal
Subtract voltage drop ($-IR$) when moving in the direction of labeled current through a resistor
Add voltage drop ($+IR$) when moving opposite the direction of labeled current through a resistor
3. Series and Parallel Resistor Combinations★★☆☆☆⏱ 3 min
Most simple circuits can be simplified by combining resistors in series or parallel to find a single equivalent resistance $R_{eq}$.
**Series resistors** are connected end-to-end, so they share the same current, and total voltage is the sum of individual voltage drops. Equivalent resistance is:
R_{series} = R_1 + R_2 + ... + R_n
**Parallel resistors** are connected across the same two points, so they share the same voltage, and total current is the sum of individual currents. Equivalent resistance is:
For two parallel resistors, this simplifies to $R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$. A useful rule: equivalent parallel resistance is always smaller than the smallest individual resistor in the group.
4. RC Circuits: Charging and Discharging★★★★☆⏱ 4 min
An RC circuit combines a resistor $R$ and capacitor $C$ in series, with predictable transient (time-dependent) behavior when a switch is flipped. The core parameter is the **time constant** $\tau$, the time required for a capacitor to charge to 63% of maximum voltage or discharge to 37% of initial voltage:
\tau = RC
When charging an initially uncharged capacitor connected to a battery: at $t=0$, the capacitor has 0 voltage and acts like a short circuit (maximum current). At $t \rightarrow \infty$, the capacitor is fully charged, acts like an open circuit (zero current). Voltage and current follow:
Voltage across capacitor: $V_c(t) = \varepsilon(1 - e^{-t/\tau})$
Current in circuit: $I(t) = I_0 e^{-t/\tau}$, where $I_0 = \frac{\varepsilon}{R}$
When discharging an initially charged capacitor connected across a resistor (no battery), both voltage and current decay exponentially: $V_c(t) = V_0 e^{-t/\tau}$, $I(t) = \frac{V_0}{R} e^{-t/\tau}$. For AP exam purposes, a capacitor is ~99% discharged after $5\tau$.
5. Power Dissipation in Circuits★★★☆☆⏱ 3 min
Power is the rate of energy transfer in a circuit, measured in Watts (W). All power dissipated by resistors is converted to heat via Joule heating. The base formula for power is:
P = VI
Substituting Ohm's law gives two alternative forms, useful for different circuit configurations:
$P = I^2 R$ (best for series circuits, where current is constant)
$P = \frac{V^2}{R}$ (best for parallel circuits, where voltage is constant)
For batteries with internal resistance $r$, total power supplied by the battery is $P_{total} = \varepsilon I$, power lost to internal heating is $P_{lost} = I^2 r$, and the remaining power is delivered to the external load.
Common Pitfalls
Why: Ohm's law only applies to materials with constant resistance; non-ohmic materials have non-linear I-V curves
Why: Failing to label current directions before writing loop equations leads to inconsistent signs
Why: Confusion between series and parallel resistance combination rules
Why: Memorizing rules backwards without understanding transient behavior
Why: Confusing the total source emf with the actual voltage across the external load