AP Physics – Current, Resistance, and Ohm’s Law

AP Physics – Current, Resistance, and Ohm’s Law

AP Physics: Current, Resistance, and Ohm’s Law – Exam-Ready Study Guide

What This Is

This topic covers how electric charge flows through materials, what resists that flow, and the simple rule (Ohm’s Law) that ties them together. On the AP exam, you’ll see circuit problems, experimental design questions, and conceptual reasoning about real-world devices like light bulbs, resistors, and power lines. A famous historical example: Thomas Edison and George Westinghouse’s "War of the Currents" (late 1800s) pitted direct current (DC) against alternating current (AC) for powering cities—highlighting how resistance and power loss shape technology.

Key Terms & Concepts

• Electric current (I): Flow of electric charge, measured in amperes (A). 1 A = 1 C/s (coulomb per second).
• Voltage (V or ?V): Electric potential difference, measured in volts (V). Think of it as "electrical pressure" pushing charge through a circuit.
• Resistance (R): Opposition to current flow, measured in ohms (?). Depends on material, length, cross-sectional area, and temperature.
• Ohm’s Law: V = I × R (Voltage = Current × Resistance). Only applies to ohmic materials (resistance stays constant with voltage).
• Resistivity (?): A material’s intrinsic resistance, measured in ?·m. Formula: R =-× (L/A), where L = length, A = cross-sectional area.
• Power (P): Rate of energy transfer, measured in watts (W). Formulas:
• P = I × V (Power = Current × Voltage)
• P = I² × R (Power = Current² × Resistance)
• P = V² / R (Power = Voltage² / Resistance)
• Series circuit: Components connected end-to-end; current is the same everywhere, but voltage divides.
• Parallel circuit: Components connected across the same two points; voltage is the same everywhere, but current divides.
• Kirchhoff’s Laws:
• Current Law (Junction Rule): Sum of currents entering a junction = sum leaving.
• Voltage Law (Loop Rule): Sum of voltage drops around a closed loop = 0.
• Superconductors: Materials with zero resistance at very low temperatures (e.g., MRI machines use them).
• Non-ohmic devices: Resistance changes with voltage (e.g., diodes, light bulbs).

Step-by-Step / Process Flow

How to Solve Circuit Problems (Ohm’s Law + Kirchhoff’s Laws)

1. Label the circuit: Draw all currents (with arrows) and voltage drops (with +/– signs).
2. Identify series/parallel parts: Simplify resistors in series (R_total = R? + R?) or parallel (1/R_total = 1/R? + 1/R?).
3. Apply Kirchhoff’s Laws:
4. Junction Rule: Write equations for current at junctions (e.g., I? = I? + I?).
5. Loop Rule: Sum voltage drops around a loop = 0 (e.g., V_battery – I×R? – I×R? = 0).
6. Solve the system of equations: Use substitution or matrices for multiple loops.
7. Check units and reasonableness: Does current increase when resistance decreases? Does power make sense?

Example: A 12 V battery powers two resistors (3-and 6 ?) in series. - Total resistance: R_total = 3 + 6 = 9 ? - Current: I = V/R = 12/9 = 1.33 A - Voltage drop across 3-resistor: V = I×R = 1.33 × 3 = 4 V

Common Mistakes

• Mistake: Assuming all materials obey Ohm’s Law. Correction: Ohm’s Law only works for ohmic materials (e.g., metals at constant temperature). Non-ohmic devices (e.g., diodes) have R that changes with V.

• Mistake: Mixing up series and parallel rules. Correction:

• Series: Current same, voltage divides.

• Parallel: Voltage same, current divides.

• Mistake: Forgetting units (e.g., using k? instead of-in calculations). Correction: Always convert to base units (e.g., 5 k? = 5000 ?).

• Mistake: Ignoring internal resistance of batteries. Correction: Real batteries have small resistance (r); terminal voltage = V =-– I×r (where ? = emf).

• Mistake: Misapplying power formulas. Correction: Use P = I²R for heat loss in resistors, P = IV for general power.

AP Exam Insights

1. FRQs often test:
2. Experimental design: Measuring resistance with a voltmeter/ammeter (e.g., "Explain how to determine the resistivity of a wire").
3. Circuit analysis: Multi-loop circuits with Kirchhoff’s Laws (e.g., "Calculate the current through R?").

4. Conceptual reasoning: Why does a light bulb’s resistance increase when it’s on? (Temperature dependence of resistivity.)

5. Multiple-choice traps:

6. Non-ohmic devices: A question might show a V vs. I graph with a curve (not a straight line) and ask about resistance.
7. Power dissipation: "Which resistor dissipates the most power?" (Answer depends on I and R; use P = I²R or P = V²/R.)

8. Parallel vs. series: "What happens to total resistance if you add a resistor in parallel?" (It decreases.)

9. Tricky distinction:

10. Resistivity (?) vs. Resistance (R): Resistivity is a material property; resistance depends on shape (R = ?L/A).

Quick Check Questions

1. Multiple Choice: A 6-resistor and a 3-resistor are connected in parallel to a 9 V battery. What is the current through the 3-resistor? (A) 1 A (B) 2 A (C) 3 A (D) 6 A Answer: (C) 3 A. Voltage across parallel resistors is the same (9 V), so I = V/R = 9/3 = 3 A.

2. Short FRQ: A student measures the current through a resistor as 0.5 A when the voltage is 6 V. Is the resistor ohmic? Justify your answer. Answer: Yes, because R = V/I = 6/0.5 = 12 ? is constant (Ohm’s Law holds).

3. Multiple Choice: Which of the following changes would decrease the resistance of a wire? (A) Increasing its length (B) Increasing its temperature (C) Increasing its cross-sectional area (D) Using a material with higher resistivity Answer: (C) Increasing its cross-sectional area. R = ?L/A; larger A-smaller R.

Last-Minute Cram Sheet

1. Ohm’s Law: V = I × R (only for ohmic materials).
2. Resistivity formula: R = ?L/A (? = resistivity, L = length, A = area).
3. Power formulas: P = IV = I²R = V²/R.
4. Series resistors: R_total = R? + R? + ... (current same).
5. Parallel resistors: 1/R_total = 1/R? + 1/R? + ... (voltage same).
6. Kirchhoff’s Current Law: Sum of currents in = sum out.
7. Kirchhoff’s Voltage Law: Sum of voltage drops = 0 in a loop.
8. Non-ohmic devices: Diodes, light bulbs (resistance changes with voltage).
9. Superconductors: Zero resistance at low temps (e.g., MRI machines).
10. Internal resistance: Terminal voltage = ? – Ir (? = emf, r = internal resistance).