---
title: "Non-Ideal Battery — AP Physics C: E&M Definition & Guide"
description: "A non-ideal battery has internal resistance, so its terminal voltage drops below the EMF when current flows. Learn V = ε − Ir and how AP exams test it."
canonical: "https://fiveable.me/ap-physics-c-e-m/key-terms/non-ideal-battery"
type: "key-term"
subject: "AP Physics C: E&M"
unit: "Unit 11"
---

# Non-Ideal Battery — AP Physics C: E&M Definition & Guide

## Definition

A non-ideal battery is a real battery modeled as an ideal EMF source in series with an internal resistance r, so its terminal voltage V = ε − Ir is less than the EMF whenever current flows (Topic 11.2, Electric Circuits).

## What It Is

An [ideal battery](/ap-physics-c-e-m/unit-11/5-compound-direct-current-circuits/study-guide/lvbJLaPd4EqBAUf6 "fv-autolink") would hold a perfect, constant [potential difference](/ap-physics-c-e-m/key-terms/potential-difference "fv-autolink") no matter how much current you pull from it. Real batteries can't do that. A non-ideal battery is modeled as an ideal EMF source (ε) in series with a small internal resistance (r) hidden inside the battery itself. When current I flows, some of the EMF gets "used up" pushing charge through that internal resistance, so the voltage you actually measure across the terminals is V = ε − Ir.

The key consequence is that [terminal voltage](/ap-physics-c-e-m/key-terms/terminal-voltage "fv-autolink") depends on the current. With the circuit open (no current), the terminal voltage equals the EMF exactly. As you draw more current, the terminal voltage sags. In the extreme case of a short circuit, the only thing limiting current is r, so I_max = ε/r. On a schematic, you draw the internal resistance as a regular resistor in series with the battery symbol, and then Kirchhoff's rules handle the rest. Nothing new is required, just one extra resistor in the loop.

## Why It Matters

Non-ideal batteries live in Topic 11.2, Electric Circuits, and they're the bridge between idealized circuit theory and real measurements. Once you add [internal resistance](/ap-physics-c-e-m/key-terms/internal-resistance "fv-autolink"), every Kirchhoff loop analysis, power calculation, and graph interpretation gains a layer the exam loves to test. For example, the slope of a terminal voltage vs. current graph is −r and the y-intercept is ε, which is exactly the kind of linearization [AP Physics C](/ap-physics-c-e-m "fv-autolink") experimental-design questions are built on. It also explains physical behavior, like why a battery's measured voltage drops when you connect a low-resistance load, and why batteries get warm. Power dissipated internally (I²r) is energy that never reaches the rest of the circuit.

## Connections

### [Open Circuit (Unit 11)](/ap-physics-c-e-m/key-terms/open-circuit)

With the circuit open, no current flows, so the Ir term vanishes and the terminal voltage equals the EMF. That's how you measure ε experimentally, with a [voltmeter](/ap-physics-c-e-m/key-terms/voltmeter "fv-autolink") and nothing else connected.

### [Short Circuit (Unit 11)](/ap-physics-c-e-m/key-terms/short-circuit)

Short the terminals of a non-ideal battery and the internal resistance becomes the entire circuit. [Current](/ap-physics-c-e-m/unit-11/4-electric-power/study-guide/u2cRqQTlthIAJtwp "fv-autolink") maxes out at I = ε/r, and all the power dumps into the battery itself, which is why shorted batteries get dangerously hot.

### [Circuit Schematic (Unit 11)](/ap-physics-c-e-m/key-terms/circuit-schematic)

On a schematic, a non-ideal battery is just two symbols glued together, an ideal EMF source plus a series [resistor](/ap-physics-c-e-m/key-terms/resistor "fv-autolink") labeled r. Once you draw it that way, Kirchhoff's loop rule treats r like any other resistor.

### [Parallel Combination (Unit 11)](/ap-physics-c-e-m/key-terms/parallel-combination)

Adding loads in parallel lowers the equivalent external resistance, which raises the total current from the battery. More current means a bigger Ir drop, so the terminal voltage sags as you plug in more devices.

## On the AP Exam

Multiple-choice questions often hand you a terminal voltage vs. current graph and ask you to read off ε (the intercept) and r (the negative of the slope), or ask how terminal voltage changes when a switch closes or a resistor is added. FRQs fold internal resistance into Kirchhoff's loop rule, where you treat r as one more series resistor in the loop equation. Released circuit FRQs, like the 2022 capacitor-discharge experiment, show the pattern College Board favors here, which is connecting a circuit model to measured data. Be ready to (1) write V = ε − Ir from a loop equation, (2) explain why a voltmeter reads less than ε when current flows, and (3) compute power lost internally as I²r versus power delivered to the external circuit.

## non-ideal battery vs EMF vs. terminal voltage

EMF (ε) is the fixed potential difference the battery's chemistry provides, while terminal voltage is what you actually measure across the terminals. They're equal only when no current flows. Once current I flows, terminal voltage drops to ε − Ir. A common error is plugging ε into Ohm's law for the external circuit when you should be using the terminal voltage.

## Key Takeaways

- A non-ideal battery is modeled as an ideal EMF source in series with an internal resistance r, so terminal voltage is V = ε − Ir.
- Terminal voltage equals the EMF only when no current flows, which is why an open-circuit voltmeter reading gives you ε directly.
- On a graph of terminal voltage versus current, the y-intercept is the EMF and the slope is −r.
- The maximum current a battery can deliver is ε/r, which occurs when the terminals are short-circuited.
- Power dissipated inside the battery is I²r, so increasing the current wastes more energy as heat before it ever reaches the external circuit.
- In Kirchhoff's loop rule, treat internal resistance exactly like any other series resistor in the loop.

## FAQs

### What is a non-ideal battery in AP Physics C?

It's a real battery modeled as an ideal EMF source in series with an internal resistance r. Because of r, the terminal voltage V = ε − Ir is less than the EMF whenever current flows.

### Is terminal voltage always less than EMF?

No. Terminal voltage equals the EMF when no current flows (open circuit). It only drops below ε when current is being drawn, and the drop equals Ir.

### How is a non-ideal battery different from an ideal battery?

An ideal battery maintains a constant terminal voltage equal to its EMF no matter the current. A non-ideal battery has internal resistance, so its terminal voltage sags as current increases, following V = ε − Ir.

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

Plot terminal voltage versus current. The graph is a line with y-intercept ε and slope −r, so the internal resistance is the negative of the slope. This linearization shows up in AP Physics C experimental-design questions.

### What happens when you short-circuit a non-ideal battery?

The internal resistance becomes the only resistance in the circuit, so the current spikes to its maximum value I = ε/r. All the power (I²r) dissipates inside the battery, which is why shorted batteries overheat.

## Related Study Guides

- [11.2 Electric Circuits](/ap-physics-c-e-m/unit-11/2-electric-circuits/study-guide/17WyJIXaesWwOEX8)

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