AP Physics 2 Ohm's Law and Resistance

« Back to AP Physics Guide / Unit 11: Electric Circuits

Simple DC circuit illustration with battery and lightbulb.

In Unit 11, we study how charges flow through materials to perform work. Understanding the relationship between voltage, current, and resistance is essential for analyzing complex compound circuits.

1. Electric Current & Current Density (Topics 11.1 & 11.2)

Current ( $I$ ) is the rate at which charge flows through a cross-section of a conductor. In AP Physics 2, we use conventional current, which flows from the positive terminal to the negative terminal.

$I = \frac{\Delta Q}{\Delta t}$

Current is measured in Amperes (A).

Current Density ( $J$ ): While current describes total flow, $J$ describes the flow per unit area ( $J = I/A$ ). This helps us understand how charge distribution changes when the thickness of a wire changes.

2. Resistance & Resistivity (Topic 11.3)

Resistance ( $R$ ) is the opposition to current flow. It is determined by the material’s resistivity ( $\rho$ ), its length ( $L$ ), and its cross-sectional area ( $A$ ).

$R = \rho \frac{L}{A}$

Resistance increases with length but decreases with a larger cross-sectional area.

3. Ohm’s Law & Power (Topic 11.4)

For Ohmic materials, current is directly proportional to the voltage applied and inversely proportional to the resistance. Electric Power ( $P$ ) is the rate at which energy is dissipated by a resistor.

$\Delta V = IR \quad \text{and} \quad P = I\Delta V = I^2 R = \frac{(\Delta V)^2}{R}$

Power is measured in Watts (W) or Joules per second (J/s).

AP Exam Tip: Not all materials follow Ohm’s Law. Devices like diodes and filaments are non-ohmic—their resistance changes with voltage or temperature.

4. Quick AP Practice

📚 Unit 11 Practice Problems

1. If you double the length of a wire but keep the material and area the same, what happens to its resistance?

Check Answer

Since $R \propto L$ , doubling the length doubles the resistance ( $2R$ ).

2. A $10 \, \Omega$ resistor is connected to a $20 \, \text{V}$ battery. What is the power dissipated?