5.1.11

# Emf & Internal Resistance

Test yourself

## Electromotive Force

Electromotive force or EMF is the total voltage produced by the cell. Not all of this is seen by the circuit.

### Internal resistance

• A cell produces a set amount of voltage, this voltage is what makes the current flow around the circuit.
• Some of this voltage has already been used by the internal resistance of the cell itself.
• EMF is measured in Volts (V).

### Calculations

• The EMF of a cell can be calculated by combining the internal resistance of the cell and the resistance of the circuit.
• The equation for the EMF is:
• EMF = (Internal resistance + circuit resistance) x current
• ${\epsilon}=(r+R)I$
• Where ${\epsilon}$ is the EMF, r is the internal resistance and R is the circuit resistance.

## Internal Resistance

The internal resistance of a cell causes a loss of voltage before the circuit begins.

### Sources of resistance

• Most cells have some internal resistance, they reduce the voltage output of the cell before it reaches the circuit.
• Internal resistance arises because the cell is made up of chemicals which will resist the flow of charge.

### Inside a cell

• The inside of a cell is very complex and different chemicals have different resistances.
• A cell can be thought of as a swirl of chemicals which generate power but also provide resistance.

## Investigating Internal Resistance

In order to know what the internal resistance of a cell is we must conduct an experiment.

### Finding the emf

• Firstly connect the cell to two wires, one to the positive and one to the negative terminal.
• Use a voltmeter to measure the voltage between these two wires, this is known as the open-circuit voltage and is the same as the emf.

### Finding the current and voltage

• Next, connect a resistor of known resistance between the two wires.
• Use a voltmeter to measure the voltage across the resistor.
• Use an ammeter to measure the current flowing in the circuit.

### Calculation

• The current, voltage, emf and internal resistance are linked in this equation:
• Voltage = emf - (current x internal resistance)
• $V={\epsilon}-Ir$
• We can rearrange this to give the internal resistance:
• $r=\frac{{\epsilon}-V}{I}$