---
title: "Nonideal Battery — AP Physics C: E&M Definition & Guide"
description: "A nonideal battery is an emf source in series with internal resistance r, so terminal voltage drops to V = ε − Ir when current flows. Core to Topic 11.5 circuits."
canonical: "https://fiveable.me/ap-physics-c-e-m/key-terms/nonideal-battery"
type: "key-term"
subject: "AP Physics C: E&M"
unit: "Unit 11"
---

# Nonideal Battery — AP Physics C: E&M Definition & Guide

## Definition

A nonideal battery is a real battery modeled as an ideal emf source ε in series with an internal resistance r, so when current I flows, its terminal voltage drops below the emf according to V = ε − Ir (AP Physics C: E&M, Topic 11.5).

## What It Is

A nonideal battery is how [AP Physics C: E&M](/ap-physics-c-e-m "fv-autolink") models a *real* battery. On paper, you draw it as two things glued together inside one package. The first is an ideal emf source ε that always supplies the same [potential difference](/ap-physics-c-e-m/key-terms/potential-difference "fv-autolink"). The second is a small internal resistance r in series with it. The chemicals and materials inside any real battery resist current flow, and r captures that.

The payoff is one equation. When current I flows out of the battery, the [terminal voltage](/ap-physics-c-e-m/key-terms/terminal-voltage "fv-autolink") (what a voltmeter actually reads across the battery's terminals) is V = ε − Ir. Some of the emf gets "used up" inside the battery itself as the Ir drop across the internal resistance. Draw more current, lose more voltage. That's why a car battery reads lower while the starter motor is cranking, and why a 12 V battery might only deliver 11.5 V or 10 V to a circuit. With zero current flowing (an open circuit), V = ε, which is exactly how you'd measure the emf in the first place.

## Why It Matters

Nonideal batteries live 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**. Once a circuit has [internal resistance](/ap-physics-c-e-m/key-terms/internal-resistance "fv-autolink"), you can't just slap ε across the external resistors. You have to treat r as one more series resistor in your Kirchhoff loop, which changes the current, the terminal voltage, and the power delivered to everything downstream. The model also unlocks two classic exam moves. First, finding ε and r from data (give me two current-voltage pairs, solve the system). Second, maximum power transfer, where the external load gets the most power when R = r. Internal resistance is also where efficiency questions come from, since power dissipated as I²r inside the battery is power the circuit never sees.

## Connections

### [Internal resistance (Unit 11)](/ap-physics-c-e-m/key-terms/internal-resistance)

Internal resistance r is literally the thing that makes a battery nonideal. The whole model is just an ideal battery plus r in series, so every nonideal battery problem starts by treating r like one more [resistor](/ap-physics-c-e-m/key-terms/resistor "fv-autolink") in the loop.

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

Terminal voltage is the observable consequence of being nonideal. V = ε − Ir means the [voltage](/ap-physics-c-e-m/key-terms/voltage "fv-autolink") at the terminals depends on how much current is flowing, which is why the same battery can read 12 V unloaded and 10 V under load.

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

A nonideal battery driving an external resistance R is secretly a [voltage divider](/ap-physics-c-e-m/key-terms/voltage-divider "fv-autolink"). The emf splits between r and R in proportion to their resistances, so the terminal voltage is just the divider output V = εR/(R + r).

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

Internal resistance is always in series with the emf, never in parallel. That's why you add r directly to the external equivalent resistance when finding the circuit current with I = ε/(R + r).

## On the AP Exam

Multiple-choice questions hit this term from a few angles. One classic stem describes a 12 V battery whose terminals read only 11.5 V under load and asks you to name or explain it (answer: nonideal battery, the missing 0.5 V is the Ir drop across internal resistance). Another asks how the power delivered to an external network changes if you swap the nonideal battery for an ideal source with the same voltage. You'd recompute the current without r and compare, and the power goes up because the external circuit now gets the full emf. A third favorite is maximum power transfer, which asks for the external resistance R that maximizes power delivered. The answer is R = r, and it's worth just memorizing alongside knowing the calculus derivation (maximize P = ε²R/(R + r)²). On FRQs, expect to write Kirchhoff's loop rule with r included, solve for current with I = ε/(R + r), or extract ε and r from a graph of terminal voltage versus current, where the y-intercept is ε and the slope is −r.

## nonideal battery vs Ideal battery

An ideal battery has zero internal resistance, so its terminal voltage equals its emf no matter how much current flows. A nonideal battery has internal resistance r, so its terminal voltage sags below the emf by Ir whenever current flows. They only behave identically in an open circuit, when I = 0 and V = ε for both.

## Key Takeaways

- A nonideal battery is modeled as an ideal emf source ε in series with an internal resistance r.
- Terminal voltage under load is V = ε − Ir, so it drops below the emf whenever current flows and equals the emf only when no current flows.
- To analyze a circuit, add r to the external equivalent resistance, so the current is I = ε/(R + r).
- Maximum power is delivered to an external load when the load resistance equals the internal resistance, R = r.
- Power dissipated inside the battery is I²r, which is why a nonideal battery delivers less power to the external circuit than an ideal source with the same voltage.
- On a graph of terminal voltage versus current, the y-intercept gives the emf and the slope gives −r.

## FAQs

### What is a nonideal battery in AP Physics C: E&M?

It's the model for a real battery, drawn as an ideal emf source ε in series with an internal resistance r. When current I flows, the terminal voltage drops to V = ε − Ir instead of staying at the full emf.

### Is terminal voltage always less than emf for a nonideal battery?

No. Terminal voltage equals the emf when no current flows (open circuit), and it's less than the emf by Ir while the battery discharges. It can even exceed the emf if the battery is being charged, since current then flows the other way.

### How is a nonideal battery different from an ideal battery?

An ideal battery has zero internal resistance, so it always outputs exactly its emf. A nonideal battery loses Ir volts internally, so a 12 V battery might only put 10 V across the external circuit. Replacing a nonideal battery with an ideal one of the same voltage increases the current and the power delivered to the load.

### How do I find the internal resistance of a battery from a circuit problem?

Use V = ε − Ir with known values, or rearrange the loop rule. For example, if a 12 V emf battery delivers a terminal voltage of 10 V while pushing 1 A, then r = (12 − 10)/1 = 2 Ω. On a V vs. I graph, r is the magnitude of the slope.

### When does a nonideal battery deliver maximum power to a resistor?

When the external resistance equals the internal resistance, R = r. You can prove it by maximizing P = ε²R/(R + r)² with calculus, which is a classic AP Physics C: E&M result from Topic 11.5.

## 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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