Peoples Physics Concepts

http://www.ck12.org Chapter 13. Electric Circuits: Batteries and Resistors

13.7 Internal Resistance

• Compare Emf and Voltage.


• Calculate the internal resistance of a battery.

Students will learn the difference between Emf and Voltage (i.e. ideal voltage and the output voltage) and how to

calculate the internal resistance of a battery.

Key Equations

Vterminal=Em f−Ir

The terminal voltage (or ’output voltage’) is equal to the emf (it’s ’ideal voltage’) minus the voltage drop across the
internal resistance.

Guidance

A battery is a voltage source. A battery can be thought of as a perfect voltage source with a small resistor (called

internal resistance) in series. The electric energy density produced by the chemistry of the battery is calledemf,but

the amount of voltage available from the battery is calledterminal voltage. The terminal voltage equals the emf

minus the voltage drop across the internal resistance (current of the external circuit times the internal resistance). In

practice, if you short circuit a battery and measure its voltage you will see the voltage is less than what is marked

on it and what it can produce when outputting smaller currents. The short circuit of the battery, makes it pump out

a lot of current and then the voltage drop over the internal resistance gets large (V = Ir) which in turn reduces the

terminal voltage.

Example 1

You have a battery with an EMF of 5 V and an unknown internal resistance. You hook the battery up to a circuit

with one 3Ωresistor and measure the current through the resistor to be 1.5 A. What is the internal resistance of the

batter and how much power is the battery’s resistance dissipating.

Solution

To start this problem we’ll first find the terminal voltage of the battery using the information we know about the

resistor. We know the voltage drop across the resistor must be equal to the terminal voltage because there the total

change in voltage must be over the whole circuit.

V=IR

V= 1 .5 A∗ 3 Ω

V= 4 .5 V