Unit 4: Electric Circuits

Executive Summary

Circuits move charge; Ohm's law and Kirchhoff's rules predict every current and voltage.

Current and resistance

Current I = rac{\Delta Q}{\Delta t} (amperes). Ohm's law: $V = IR$. Resistance $R = \rho L/A$ — longer, thinner, and more resistive materials raise R. Power: $P = IV = I^2R = V^2/R$.

Series and parallel

Series: current identical, voltages add, $R_{eq} = R_1 + R_2$. Parallel: voltage identical, currents add, $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$. Parallel resistors always reduce equivalent resistance.

Kirchhoff's rules

Junction rule: current in = current out (charge conservation). Loop rule: voltage rises equal drops around any closed loop (energy conservation). Batteries add voltage in series; identical batteries in parallel keep voltage but extend life.

Exam traps

Adding a resistor in parallel LOWERS total resistance. Brightness tracks power. Ammeters connect in series, voltmeters in parallel. A battery's terminal voltage drops under load due to internal resistance. Kirchhoff's loop rule is just energy conservation in disguise.