Internal Resistance, EMF and Oscilloscopes

What we are going to achieve today

• Creating power from lemons• Find out about internal resistance of batteries• Know what is the electromotive force is• Use an oscilloscope to measure the frequency

and voltage from an signal generator

Using lemons, limes and potatoes to power an LED

zinc copper

Making Batteries

There is nothing special about batteries – but these have a high internal resistance.

Rl

What do you think the best way to minimise the internal resistance of your battery?Think about resistivity (lemon is a poor conductor)

Batteries

What is the main energy transfer in a battery?

Electrical energy

This is powered by two 1.5 V AA cells in series - what is the supply voltage?

What is the emf of the supply?

After a while the battery needs to be replaced; why?

What determines how quickly it runs down?

What determines how much current is drawn from the supply?

EMF Electromotive Force

• EMF is the external work expended per unit of charge to produce an electric potential

difference across two open-circuited terminals

This is the same definition as voltage but on an open circuit (no current flow)

Why is this definition important?

Batteries have internal resistance

The circuit now has two resistors in

The internal resistance of the battery, r is very small.

R is much larger

The total resistance of this circuit is Rtotal = R +r

I = E / (R+r)

Batteries have internal resistance

As charge goes around the circuit the sum of emfs must equal the sum of voltage drops leading to

EMF = I R + I r

The terminal voltage is equal to I R so this can be rearranged to give:

V = E – I r

and interpreted as terminal voltage = emf – ‘lost volts’

R -small

Rtotal = r + R -small

The current will now be larger as the total resistance of the circuit is much lower

The voltage lost across r

V = I(large)r

The voltage lost will now be a problem

This case is of a small load resistance connected to a battery is seen in a starter motor on a car

http://www.youtube.com/watch?v=al6Yz3Nv7dY

http://www.youtube.com/watch?v=Ut7yBdIehYY&NR=1

Starter motor on a conventional carThe headlamps are connected in parallel across a twelve-volt battery.

The starter motor is also in parallel controlled by the ignition switch.

Since the starter motor has a very low resistance it demands a very high current (say 60 A).

The battery itself has a low internal resistance (say 0.01 Ω).

The headlamps themselves draw a much lower current (they have a higher resistance)

Lamp

R

Starter motor

Ignition switch

12V

What will happen to the lights?

Quick Questions

1. A 9.0 V battery has an internal resistance of 12.0 . (a) What is the potential difference across its terminals when it is supplying a

current of 50.0 mA?

(b)What is the maximum current this battery could supply?

(c)Draw a sketch graph to show how the terminal potential difference varies with the current supplied if the internal resistance remains constant. How could the internal resistance be obtained from the graph?

2. A cell in a deaf aid supplies a current of 25.0 mA through a resistance of 400 . When the wearer turns up the volume, the resistance is changed to 100 and the current rises to 60 mA. What is the emf and internal resistance of the cell?

V = E – I r V = IRE = I(R +r)

You need to set up a simultaneous equation

Answers1. (a) pd = E – I r = 9 – (50 x 10-3 x 12) = 8.4 V (b) Max current = E/r = 9 / 12 = 0.75 A

2. E = I(R +r)E = 25 x 10-3 (400 + r) and E = 60 x 10-3 (100 +

r)So25 x 10-3 (400 + r) = 60 x 10-3 (100 + r) so r =

114.3 E = 10 + (25 x 10-3 x 114.3) = 12.86 V

I

V

OscilloscopeUse the signal generator to create A/C (alternating current) on the Oscilloscope

Draw 2 signals of 2 different frequencies

Work out the frequency of the Oscilloscope

Add the magnitude of the waveheight