Internal Resistance

Part of the Electricity and Magnetism section of Coddy's Physics journey. Lesson 26 of 51.

A real battery has an EMF ε and an internal resistance r:

$\varepsilon = I(R + r)$

A battery with internal resistance

The voltage at its ends drops as the current grows:

$V = \varepsilon - Ir$

Its efficiency is $\frac{V}{\varepsilon} = \frac{R}{R + r}$ .

Challenge

A battery with EMF $12\ \mathrm{V}$ and internal resistance $0.5\ \mathrm{\Omega }$ is connected to a $5.5\ \mathrm{\Omega }$ resistor. What is the voltage $V$ at the battery's ends?

Try it yourself

Solve for $V$

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Electricity and Magnetism

1Electric Charge and Force

Electric Charge Coulomb's Law Several Charges Recap - Charges in a Line

4Charged Conductors

The Charged Sphere Connecting Spheres Recap - Beam Between Plates

7Real Batteries

Internal ResistanceThe Variable Resistor Ammeters and Voltmeters Recap - Flashlight

10Magnetic Fields

Magnets and Magnetic Fields Field of a Wire Loops and Solenoids Recap - Electromagnet

2The Electric Field

The Electric Field Field of Several Charges The Uniform Field A Charge in a Uniform Field Recap - Stopping a Proton

5Capacitors

The Capacitor Combining Capacitors Changing a Capacitor Recap - Camera Flash

8Kirchhoff's Laws

The Junction Rule The Loop Rule Solving Two Loops Recap - Charging a Battery

11Magnetic Forces

Force on a Moving Charge Circles in a Field Force on a Wire Two Parallel Wires Recap - Current Balance

3Energy and Potential

Electric Potential Energy Electric Potential Field and Potential Recap - Accelerating Ions

6Current and Resistance

Current and Voltage Resistance and Ohm's Law Series and Parallel Electric Power Recap - Fairy Lights

9Capacitors in Circuits

A Capacitor in a Circuit Charging a Capacitor Discharging a Capacitor Recap - Defibrillator

12Induction

A Rod Moving in a Field Magnetic Flux Faraday's Law Lenz's Law Recap - Generator