---
title: "I-V Graph — AP Physics 2 Definition & Exam Guide"
description: "An I-V graph plots current vs. potential difference. In AP Physics 2, a straight line through the origin means ohmic behavior, and the slope equals 1/R."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/i-v-graph"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 11"
---

# I-V Graph — AP Physics 2 Definition & Exam Guide

## Definition

An I-V graph plots current (I) on the vertical axis against potential difference (ΔV) on the horizontal axis for a circuit element. Because I = ΔV/R, an ohmic resistor produces a straight line through the origin whose slope equals 1/R, so a steeper line means lower resistance.

## What It Is

An I-V graph is the standard way to show how a [circuit element](/ap-physics-2-revised/unit-11/2-simple-circuits/study-guide/LROjr9EJ6hjfPDMC "fv-autolink") responds when you change the [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink") across it. You put current on the y-axis, potential difference on the x-axis, and plot the data. Since Ohm's law says I = ΔV/R, the graph is really a picture of Ohm's law. If the element is **ohmic** (constant resistance for all currents), the data falls on a straight line through the origin, and the slope of that line is 1/R. Steep line, small resistance. Shallow line, big resistance.

The graph also tells you when Ohm's law *breaks*. A device whose I-V curve bends (like a light bulb filament [heating](/ap-physics-2-revised/unit-9/3-thermal-energy-transfer-and-equilibrium/study-guide/B2UC1jOK2bqVTMMH "fv-autolink") up) is non-ohmic, meaning its resistance changes with current. That connects directly to the CED point that resistivity of a conductor typically increases with temperature. A resistor converting electrical energy to thermal energy can literally change its own resistance, and the curving graph is the evidence.

## Why It Matters

This lives in **Topic 11.3 (Resistance, Resistivity, and Ohm's Law)** in **[Unit 11](/ap-physics-2-revised/unit-11 "fv-autolink"): Electric Circuits**. It directly supports learning objective **11.3.B**, which asks you to describe the electrical characteristics of circuit elements. The CED is explicit that the resistance of an ohmic element can be determined from the slope of a graph of current versus potential difference. It also leans on **11.3.A**, since the resistance you read off the graph is set by the object's physical properties through R = ρℓ/A. [AP Physics 2](/ap-physics-2-revised "fv-autolink") is heavy on graph interpretation and experimental reasoning, so being able to look at an I-V plot and immediately state the resistance, or argue whether the material is ohmic, is one of the highest-value skills in this unit.

## Connections

### Ohm's Law, I = ΔV/R (Unit 11)

The I-V graph is [Ohm's law](/ap-physics-2-revised/unit-11/3-resistance-resistivity-and-ohms-law/study-guide/y0ZmKqhOPqeLWZFa "fv-autolink") drawn as a picture. The equation I = ΔV/R has the form y = mx, so the slope of the line is 1/R. If the line is straight and passes through the origin, the element obeys Ohm's law.

### [R = ρℓ/A (Unit 11)](/ap-physics-2-revised/key-terms/r-l-a)

The slope you measure on an I-V graph isn't arbitrary. It's set by the [resistor](/ap-physics-2-revised/key-terms/resistor "fv-autolink")'s material and geometry. A longer wire or a smaller cross-sectional area raises R, which flattens the I-V line. This is how a graph connects back to the physical object.

### Resistivity and temperature (Unit 11)

When [current](/ap-physics-2-revised/unit-11/1-electric-current/study-guide/QaFR8etPqRmh5pdg "fv-autolink") heats a conductor, its resistivity usually rises, so resistance climbs as you push more current through. On the graph, the line bends over instead of staying straight. A curved I-V graph is the visual signature of temperature-dependent, non-ohmic behavior.

### Energy dissipation in resistors (Unit 11)

Resistors convert electrical energy to thermal energy, which is exactly why some devices go non-ohmic at high current. The I-V graph ties the energy story to the circuit story. The same heating that warms the resistor's environment is what curves the graph.

## On the AP Exam

Expect multiple-choice questions that hand you an I-V graph (or describe one) and ask you to extract resistance from the slope, compare two resistors by comparing slopes, or decide whether a material is ohmic. A classic stem doubles the resistance and asks what happens to the slope (it halves, because slope = 1/R). Another gives data from -10 V to +10 V and asks what observation confirms ohmic behavior (a straight line through the origin, with current reversing direction when voltage reverses). In lab-based free-response questions, you may be asked to design an experiment that varies ΔV, measures I, and uses the slope of the resulting graph to find R. Watch the axes before you compute anything, because the slope only equals 1/R when current is on the vertical axis.

## I-V graph vs V-I graph (voltage on the vertical axis)

These are the same data with the axes swapped, and that swap flips what the slope means. On an I-V graph (current vertical), slope = 1/R, so the steeper line has the SMALLER resistance. On a V-I graph (voltage vertical), slope = R, so the steeper line has the larger resistance. The single most common error on these problems is reading slope as R without checking which variable is on which axis.

## Key Takeaways

- An I-V graph plots current on the vertical axis and potential difference on the horizontal axis, so the slope of the line equals 1/R, not R.
- An ohmic material produces a straight line through the origin, which means its resistance stays constant for all currents and both directions of voltage.
- Doubling a resistor's resistance cuts the slope of its I-V graph in half, so steeper lines always belong to smaller resistances on this graph.
- A curved I-V graph signals a non-ohmic device, often because the current heats the material and raises its resistivity, which raises its resistance.
- The resistance you read from the graph is determined physically by R = ρℓ/A, so material, length, and cross-sectional area all show up in the slope.
- Always check the axes first, because swapping voltage and current flips the meaning of the slope from 1/R to R.

## FAQs

### What is an I-V graph in AP Physics 2?

It's a graph of current (y-axis) versus potential difference (x-axis) for a circuit element. The CED for Topic 11.3 states that the resistance of an ohmic element can be determined from this graph, since the slope equals 1/R.

### Is the slope of an I-V graph equal to resistance?

No. With current on the vertical axis, the slope is 1/R, the inverse of resistance. The slope only equals R on a V-I graph, where voltage is on the vertical axis. Checking the axes is step one on every one of these problems.

### How do you know if a material is ohmic from its I-V graph?

The graph must be a straight line passing through the origin, and the relationship should hold for both positive and negative voltages (for example, data from -10 V to +10 V falling on one line). Any curve means resistance is changing with current, so the material is non-ohmic.

### Why is a light bulb's I-V graph curved?

The filament heats up as current flows, and the resistivity of a conductor typically increases with temperature. Rising resistance means each extra volt produces less extra current, so the graph bends over instead of staying straight.

### What happens to the I-V graph if you double the resistance?

The slope is cut in half. Since slope = 1/R, doubling R from R to 2R drops the slope from 1/R to 1/(2R). This exact comparison shows up as a multiple-choice question, so know it cold.

## Related Study Guides

- [11.3 Resistance, Resistivity, and Ohm's Law](/ap-physics-2-revised/unit-11/3-resistance-resistivity-and-ohms-law/study-guide/y0ZmKqhOPqeLWZFa)

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