# Ohm's law without a voltmeter

##### Demonstration

An approach to Ohm's law in a quick demonstration.

#### Apparatus and materials

1.5-volt cells, new stock, 7 (see technical note)

Cell holders, 7

50 Ω resistor, approx value (see technical note)

Ammeter (0-1 amp), DC, preferably moving-coil

#### Health & Safety and Technical notes

Test the cells beforehand to make sure they are all approximately equal - since students will need assurance of that. Either connect each in turn to a resistance of about 3 ohms and try a voltmeter across it, or arrange all the cells in series with about 50 ohms and try a voltmeter across each cell in turn. Replace any cell that fails to agree with the rest.

The resistor might be a rheostat, or two rheostats connected in series. The aim is to keep the current low.

#### Procedure

a Set up the circuit shown. In the course of the experiment, restrict the time for which the current flows to a minimum.

b Explain to students that we expect a coulomb to make the same energy transfer in every cell. Then we use the effective number of cells as a measure of the energy transferred to each coulomb.

c Explain that all the cells will remain in the circuit, to maintain constant resistance.

d Record the ammeter reading with all 7 cells facing the same way.

e Reverse one cell, and read the ammeter for what is now a 5-cell transfer.

f Continue to reverse one more cell at a time until all 7 are reversed.

g Plot a graph, which serves as an introduction to Ohm's law.

#### Teaching notes

1 Is there a problem of logic in using moving-coil meters in experiments to 'test' Ohm's law? A moving coil voltmeter is made from a high resistance which obeys Ohm's law, and a milliammeter to measure the current through that resistance. The meter's dial is then labelled in volts. So Ohm's law is implicit in the instruments. In this case, that effect is reduced by assuming that each cell provides a standard unit of voltage.

2 The electromotive force is provided by seven 1.5-volt cells all in series, all kept in the circuit throughout to maintain constant resistance. But the effective e.m.f. is varied by reversing 1 cell, 2, 3, ... all the cells - thus obtaining 8 points on a graph. Assuming that each cell transfers the same amount of energy for each coulomb, the algebraic total of cells is used as an ideal voltmeter reading! Students plot that against the ammeter reading with a fixed resistance in the circuit.

3 When one of the cells is reversed, each coulomb receives the usual share of energy from the chemical supply in six of the cells. But in the reversed cell it has to pay one share from electrical energy back to chemical energy. (This assumes that the action of the cell can be reversed like that; not exactly true but quite close to true if the current is not driven backwards for much of the time.)

4 Once the experiment has been carried out with only the ammeter in the circuit, ask students what instrument they could use instead of counting the cells. They should know that a voltmeter is a cell counter. A voltmeter is then added to the circuit, arranging it to act as a cell counter which keeps track of what is happening in the resistance alone. When cells are reversed, the voltmeter keeps track of the 'algebraic' number of cells in the circuit. This experiment shows the essential behaviour described by Ohm's law.

This experiment was safety-checked in October 2006