---
title: "Internal Resistance — AP Physics C: E&M Definition"
description: "Internal resistance is the resistance inside a real battery that drops terminal voltage below emf when current flows. Key for circuit analysis in Topic 11.5."
canonical: "https://fiveable.me/ap-physics-c-e-m/key-terms/internal-resistance"
type: "key-term"
subject: "AP Physics C: E&M"
unit: "Unit 11"
---

# Internal Resistance — AP Physics C: E&M Definition

## Definition

Internal resistance (r) is the resistance inside a nonideal battery (or meter) that causes the terminal voltage to drop below the emf when current flows, following V_terminal = ε − Ir. It acts like a small resistor in series with an ideal emf source.

## What It Is

Internal resistance is the built-in [resistance](/ap-physics-c-e-m/unit-11/4-electric-power/study-guide/u2cRqQTlthIAJtwp "fv-autolink") of a real battery. An ideal battery would deliver its full emf ε to the circuit no matter what. A real battery can't, because charge moving through the battery itself loses some energy on the way out. You model this by drawing an ideal emf source in series with a small [resistor](/ap-physics-c-e-m/key-terms/resistor "fv-autolink") r, hidden inside the battery's casing.

The consequence is the single most-tested equation here: V_terminal = ε − Ir. The more current you draw, the bigger the Ir drop and the lower the [voltage](/ap-physics-c-e-m/key-terms/voltage "fv-autolink") actually available at the terminals. With no current flowing (open circuit), the terminal voltage equals the emf, which is exactly why a voltmeter across a disconnected battery reads ε. Internal resistance also shows up in measuring instruments. A voltmeter has a large internal resistance so it draws almost no current, and an ammeter or galvanometer has a small one so it barely disturbs the circuit it's measuring.

## Why It Matters

Internal resistance lives in **[Topic 11.5](/ap-physics-c-e-m/unit-11/5-compound-direct-current-circuits/study-guide/lvbJLaPd4EqBAUf6 "fv-autolink"), Compound Direct Current Circuits**. It's the detail that turns a textbook circuit into a realistic one. Once you treat the battery as ε in series with r, internal resistance just becomes one more series resistor in your Kirchhoff loop equation, so the current is I = ε/(R + r) for a simple loop. It also matters for energy accounting, since the battery wastes power at a rate I²r as heat inside itself, which is why batteries get warm under heavy load. Beyond circuit math, internal resistance is the backbone of E&M lab-design questions. Plotting [terminal voltage](/ap-physics-c-e-m/key-terms/terminal-voltage "fv-autolink") versus current gives a straight line whose y-intercept is ε and whose slope is −r, a classic experimental setup the exam loves.

## Connections

### [Terminal Voltage (Unit 11)](/ap-physics-c-e-m/key-terms/terminal-voltage)

Terminal voltage is the direct consequence of internal resistance. It's what's left of the emf after the Ir drop inside the battery, so V_terminal = ε − Ir. If r = 0 or I = 0, terminal voltage and emf are identical.

### [Nonideal Battery (Unit 11)](/ap-physics-c-e-m/key-terms/nonideal-battery)

A [nonideal battery](/ap-physics-c-e-m/key-terms/nonideal-battery "fv-autolink") is just the model that contains internal resistance. Draw it as a perfect emf source plus a small series resistor r, then solve the circuit normally. That one move converts every 'real battery' problem into a standard series-circuit problem.

### [Series Connection (Unit 11)](/ap-physics-c-e-m/key-terms/series-connection)

Internal resistance always combines in series with the external circuit, never in parallel, because all the current leaving the battery must pass through it. So the total resistance a battery 'sees' is R_external + r.

### [Voltage Divider (Unit 11)](/ap-physics-c-e-m/key-terms/voltage-divider)

A battery with internal resistance is secretly a [voltage divider](/ap-physics-c-e-m/key-terms/voltage-divider "fv-autolink"). The emf splits between r and the external resistance R, and the load only gets the fraction R/(R + r) of ε. This is why a nearly dead battery (large r) reads fine open-circuit but collapses under load.

## On the AP Exam

Multiple-choice questions hand you ε and r and ask for current, terminal voltage, or power. For example, a 9.0 V battery with r = 0.30 Ω in series with a 2.7 Ω resistor and 0.20 Ω of wire resistance is solved by treating r and the wires as ordinary series resistors. You'll also see internal resistance attached to meters, like a voltmeter with finite R_v that changes the reading across a parallel pair, or a galvanometer with resistance Rg in a Wheatstone bridge (spoiler for the bridge case: at balance, no current flows through the galvanometer, so Rg doesn't matter). On FRQs, internal resistance shows up in experimental-design contexts like the 2022 capacitor-discharge question, where circuit elements like resistors and meters have real, nonideal properties. Be ready to linearize data, identify ε as the intercept and r from the slope of a V vs. I graph, and explain in words why terminal voltage drops as current increases. Watch for the phrase 'negligible internal resistance' in problem stems, which is the exam's way of telling you to set r = 0.

## internal resistance vs terminal voltage

Internal resistance is a resistance (measured in ohms) hiding inside the battery; terminal voltage is the potential difference (measured in volts) you actually get at the battery's terminals. They're linked by V_terminal = ε − Ir. Students often write 'the terminal voltage of the battery is 9 V' when 9 V is really the emf. The emf is fixed by the battery's chemistry, but terminal voltage changes with the current because of internal resistance.

## Key Takeaways

- Model a real battery as an ideal emf source ε in series with a small internal resistance r.
- Terminal voltage follows V_terminal = ε − Ir, so it drops as the circuit draws more current.
- When no current flows, the terminal voltage equals the emf, which is why an open-circuit voltmeter reading gives you ε.
- Internal resistance adds in series with the external circuit, so for a single loop the current is I = ε/(R + r).
- The battery dissipates power inside itself at a rate I²r, energy that never reaches the external circuit.
- On a graph of terminal voltage versus current, the y-intercept is the emf and the slope is −r, a standard E&M lab-analysis setup.

## FAQs

### What is internal resistance in AP Physics C: E&M?

Internal resistance is the resistance inside a real (nonideal) battery, modeled as a small resistor r in series with an ideal emf source. It makes the terminal voltage drop below the emf according to V_terminal = ε − Ir whenever current flows.

### Is terminal voltage the same as emf?

No, not when current is flowing. The emf ε is the battery's full electrical 'push,' while terminal voltage is ε minus the Ir drop across the internal resistance. They're only equal when I = 0, like when nothing is connected or a balance condition kills the current.

### Does a voltmeter have internal resistance too?

Yes. A [voltmeter](/ap-physics-c-e-m/key-terms/voltmeter "fv-autolink") has a very large internal resistance R_v so it draws almost no current from the circuit, while an ammeter has a very small one. Exam questions test this by asking how a real voltmeter's finite resistance changes the reading across a resistor it's measuring.

### How do you find internal resistance from a graph?

Plot terminal voltage on the y-axis against current on the x-axis. The data follows V = ε − Ir, a straight line where the y-intercept is the emf and the slope is −r. This linearization move is a staple of E&M experimental FRQs.

### What does 'negligible internal resistance' mean in a problem?

It means set r = 0 and treat the battery as ideal, so the terminal voltage equals the emf exactly. Problem stems include this phrase to simplify the math; if it's missing and r is given, you must include r in your series-resistance total.

## Related Study Guides

- [11.5 Compound Direct Current Circuits](/ap-physics-c-e-m/unit-11/5-compound-direct-current-circuits/study-guide/lvbJLaPd4EqBAUf6)

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