Resistance

Resistance (R) is a measure of how much an object opposes the flow of electric current through it, determined by the material's resistivity and the object's geometry via R = ρL/A; in AP Physics 1 it connects voltage and current through Ohm's Law, V = IR.

Verified for the 2027 AP Physics 1 examLast updated June 2026

What is Resistance?

Resistance tells you how hard it is to push current through something. A high-resistance object lets only a trickle of charge through for a given potential difference; a low-resistance object lets charge flow easily. The unit is the ohm (Ω).

Resistance comes from two things. First, the material itself, captured by its resistivity (ρ). Copper has low resistivity, rubber has very high resistivity. Second, the object's shape. The formula R = ρL/A says a longer wire has more resistance (charges have to fight through more material) and a thicker wire has less resistance (more cross-sectional area means more room for charge to flow). Think of water in a pipe. A long, skinny pipe resists flow; a short, wide pipe doesn't. Once you know an object's resistance, Ohm's Law (V = IR) links it to the current that flows when you apply a potential difference across it.

Why Resistance matters in AP Physics 1

Resistance sits at the center of Unit 9 (Electric Circuits) in AP Physics 1. Topic 9.2 (Resistivity) asks you to predict how resistance changes when you change a resistor's length, area, or material. Topic 9.3 asks you to use resistance in Ohm's Law and to combine resistors in series and parallel, then analyze the resulting circuits with Kirchhoff's loop rule. You can't define a circuit (Topic 9.1) in any useful way without knowing how its resistive elements control current and divide voltage. Resistance is also the bridge to energy. The rate at which a resistor dissipates electrical energy (P = IΔV = I²R) shows up whenever the exam asks about brightness of bulbs or energy transfer in a circuit.

How Resistance connects across the course

Resistivity (Unit 9)

Resistivity is the material property; resistance is what a specific object actually has. Two copper wires share the same ρ, but the longer or thinner one has more resistance. R = ρL/A is the equation that ties them together.

Ohm's Law (Unit 9)

V = IR makes resistance the conversion factor between potential difference and current. Hold the battery voltage fixed and double the resistance, and the current gets cut in half. Most circuit MCQs are this relationship in disguise.

Series Circuit and Kirchhoff's Loop Rule (Unit 9)

Resistors in series add up (more total resistance, less current), while resistors in parallel give a smaller equivalent resistance because current has multiple paths. Kirchhoff's loop rule is how you account for the voltage each resistance drops around the loop.

Rate of Energy Transfer (Units 4 and 9)

Power dissipated in a resistor, P = I²R = (ΔV)²/R, is the circuits version of the energy ideas from Unit 4. A lightbulb's brightness is literally its power dissipation, which is why brightness-ranking questions are really resistance questions.

Is Resistance on the AP Physics 1 exam?

Resistance shows up in two big ways. First, geometry questions. The 2018 lab-based FRQ gave students cylinders of conductive dough with different lengths and cross-sectional areas and asked them to design an experiment to find resistivity, which means you need R = ρL/A cold, including how to linearize data (plot R versus L/A and the slope is ρ). Second, circuit-reasoning questions. The 2017 short FRQ asked students to compare bulb brightness across circuits with identical batteries and bulbs wired differently, which tests whether you know series resistances add (dimmer bulbs) while parallel branches each get the full battery voltage (brighter, more total current). FRQs reward paragraph-length reasoning, so practice writing 'adding the bulb in series increases total resistance, which decreases current, which decreases power dissipated in each bulb' rather than just citing a formula. Energy-conversion questions like the 2019 motor FRQ also lean on resistance when accounting for electrical energy that doesn't become mechanical energy.

Resistance vs Resistivity

Resistivity (ρ) is a property of the material alone, like density. Resistance (R) is a property of a specific object, and it depends on both the material and the object's shape through R = ρL/A. Cut a wire in half and its resistance halves, but its resistivity doesn't change at all. If a question changes length or area, it's testing resistance; if it asks what stays constant when you reshape the object, that's resistivity.

Key things to remember about Resistance

  • Resistance measures how much an object opposes current flow, and it's measured in ohms (Ω).

  • R = ρL/A means resistance increases with length and decreases with cross-sectional area, while resistivity ρ depends only on the material.

  • Ohm's Law, V = IR, connects resistance to current and potential difference, so more resistance at fixed voltage means less current.

  • Resistors in series add directly to give a larger equivalent resistance, while resistors in parallel combine to give a smaller equivalent resistance than any single branch.

  • Power dissipated by a resistor is P = I²R = (ΔV)²/R, which is what determines a lightbulb's brightness on circuit FRQs.

  • Reshaping an object changes its resistance but never its resistivity, a distinction the 2018 conductive dough FRQ tested directly.

Frequently asked questions about Resistance

What is resistance in AP Physics 1?

Resistance is a measure of how much an object opposes electric current, given by R = ρL/A and measured in ohms. It links voltage and current through Ohm's Law, V = IR, and is central to Unit 9 circuit analysis.

What's the difference between resistance and resistivity?

Resistivity (ρ) is a fixed property of the material, while resistance (R) depends on the material plus the object's length and cross-sectional area. Two wires of the same metal have the same resistivity but different resistances if their dimensions differ.

Does a longer wire have more or less resistance?

More. Resistance is proportional to length (R = ρL/A), so doubling the length doubles the resistance, while doubling the cross-sectional area cuts the resistance in half.

Do resistors in parallel increase total resistance?

No, the opposite. Adding a resistor in parallel opens another path for current, so the equivalent resistance drops below the smallest individual resistance. Only series resistors add up to a bigger total.

Why are bulbs in series dimmer than bulbs in parallel?

Series bulbs add their resistances, which lowers the current through every bulb and lowers each bulb's power (P = I²R). Parallel bulbs each get the full battery voltage, so each dissipates more power and glows brighter, which is exactly what the 2017 FRQ on three bulb circuits tested.