Inside This Unit: The Full Breakdown
This unit analyzes current, resistance, and Kirchhoff’s rules, and treats RC circuits with the differential equations that govern exponential charging and discharging.
Why it matters
RC-circuit calculus — setting up and solving the loop differential equation — is a hallmark Physics C: E&M skill.
Key concepts
- Current I = dQ/dt; resistance R = ρL/A; Ohm’s law V = IR.
- Kirchhoff’s junction (charge) and loop (energy) rules solve circuits.
- RC charging: Q(t) = Q_max(1 − e^(−t/RC)); discharging: Q(t) = Q₀e^(−t/RC).
- Time constant τ = RC; at steady state a capacitor passes no DC current.
Current, Resistance, and Kirchhoff’s Rules
Current is the rate of charge flow, and resistance depends on material and geometry (R = ρL/A). Kirchhoff’s junction rule (charge conservation) and loop rule (energy conservation) let you solve multi-loop circuits and find power dissipation P = I²R.
RC Circuits
Applying the loop rule to a resistor-capacitor circuit yields a differential equation whose solution is exponential: charging gives Q(t) = Q_max(1 − e^(−t/RC)) and discharging Q(t) = Q₀e^(−t/RC), with time constant τ = RC. At t = 0 the uncharged capacitor draws maximum current; at t → ∞ it blocks DC current.
AP exam tip
For RC problems, analyze the two limits first (t = 0 and t → ∞), then write the loop equation and identify the exponential solution and τ = RC.
Connections to other units
- Unit 3: The capacitor’s charge and energy were defined earlier.
- Unit 5: Changing currents lead into induction and inductors.
