Internal ResistanceThe hidden resistance of cells,

batteries and power supplies

• Theoretically using

V=IR

– if R is small (as it would

be in a short thick wire)

the current should be

large, really large if R

is very small

What would happen if a low resistance copper wire

is connected across the terminal of a 1.5V torch

battery?

R

VI

Lets try some figures

• For such a short and thick piece of copper

wire a resistance of 0.01 is not

unreasonable

• The battery has a voltage of 1.5 V

so theoretically;

• This is serious amount of current the amount

needed to start your car

• Enough to heat the wire red hot and melt it

• That’s not what’s happening WHY??

0.01

1.5

R

VI

150A

What’s wrong and why?

• Must be the calculation

• Either the value for V or R must be wrong,

how could we check?

– Measure R with a multimeter

– Measure V with a voltmeter

0.01

1.5

R

VI

150A

so;

• The battery has 1.5 V printed on it so let’s

measure R (R=0.001)

– That’s even worse and would make I 1500A ( )

• So what about the voltage of the battery?

– When its connected to the wire the voltage dropped

– Why??

0.001

1.5I

Internal Resistance of Batteries

and Power Supplies

• Batteries and power

supplies behave as if

they have a series

resistor inside them.

EMF

• When the battery or power

supply is not connected to a

circuit (no current drawn) the

voltage is at its theoretical

maximum

• This voltage is called the

EMF (electro motive force) of

the battery or power supply

(symbol εo ).

V

0

Terminal Voltage

•As soon as the cell, battery or power supply is attached to a circuit current flows.

•This current passes through the internal resistance and uses some of the energy (voltage) provided by the cell, battery or power supply (V=IR)

•So the voltage left for the circuit, the terminal voltage (VT) is the EMF minus the voltage loss across the internal resistance

IntRes0 VVT or because V=IR

IRVT 0

V

V

VT

VIntRes

Effect in Circuits

• The greater the current

drawn by the circuit the

lower the terminal voltage

(as more current flows it

passes through the internal

resistance and more energy

(voltage) is lost (V=IR))

• Older or flat batteries

have a higher internal

resistance than new or

fully charged batteries

(steeper line on graph)

Terminal Voltage of a Battery

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1 1.2

Current (A)V

olt

ag

e (

V)

Older or flatter battery

Examples

1. When a 1.5V cell is connected to a 3.0Ω load resistor the terminal voltage drops to 1.0 V. Calculate the internal resistance of the cell.

1.5Ω

2. As a student starts her car the 12.0V emf of the car battery drops to 8.0V. If the current drawn is 150A calculate the internal resistance of the battery.

0.027Ω

3. A 9.0V battery is connected to a smoke alarm. The alarm has a resistance of 630Ω and draws a current of 14mA. Find the internal resistance of battery.

13Ω

Concept Questions

• When a car has a flat battery why wont it start the car?

• What measurable differences are there between a flat and fully charged battery?

• Dry cells and batteries have a relatively high internal resistance. Explain why they are of limited use for low resistance circuits that require a terminal voltage close to the emf?

• What happens to the terminal voltage of a cell as it goes flat

• What happens to the emf of a cell as it goes flat?

• How would you test a battery to see if it is flat?

Examples

• ESA, Activity 13B, Pg 210

• ABA Pg 136-138

Assignment

• That's an excellent question! Measuring internal resistance is a little more complicated. In general, the internal resistance of a battery is not a fixed value. It varies over time as the battery loses energy and also varies depending on the load, or how much current is drawn from the battery. Engineers refer to this as a non-linear resistance. You might also find that if really load down a battery, the internal resistance changes dramatically. In order to fully characterize the internal resistance, we need to take measurements over time and for different loads. The result is a set of graphs, each plotting values of resistance as a function of load current. This can be an involved process, depending on how much data you want. We can, however, get an estimate of the internal resistance by taking only two measurements with a voltmeter. First, we need to measure the "open circuit" voltage of the battery. This is simply the voltage at the battery terminals when no current is being drawn. Practically, it's hard to measure voltage without drawing some current, but most voltmeters have a high enough input resistance that it can be neglected. So we first measure the open circuit voltage, Vo. Let's say it's 0.9 volts, as in your case. Now we need to load down the battery and measure the voltage at the battery terminals again, let's call that Vl. Let's call the load resistance Rl. Given all those values, the equation for the internal resistance (Ri) of the battery is: Equ 1: Ri = Rl * ((Vo/Vl) - 1) You can derive this equation from the equation for a voltage divider: Equ 2: Vl = Vo * Rl / (Ri + Rl) This equation can be derived from application of Ohm law and Kirchoffs law. You can find that information from any text on electric circuit theory. Now we need to choose a value of Rl that gives us good numbers. From inspection of equ 2, we can observe that if Rl equals Ri, the load voltage will be exactly half of the open circuit voltage. This trick is commonly used if you have a variable resistor within the range of internal resistance. This is not always possible, so you might have to use several fixed resistors of different values. You will probably find that typical alkaline cells tend to have relatively low internal resistances when they are new. It's probably in the range of an ohm or so. You will probably need a resistor that is not more than 10 times that value to make good measurements. If you can find a 10 ohm resistor that's OK. Of course, you should start with higher values to see the effects. Start with 100 Ohms and see what you get. Then try lower values and run the calculations again. You can enter your values into a spreadsheet and plot the results. A word of caution: be careful when using low value resistors with good batteries, the current draw will be high enough the heat up the resistor (and the battery!).