e.m.f. and internal resistance

e.m.f. is an abbreviation for electromotive force.

When charge flows through a cell it is given energy by the cell.

The number of joules of energy given to each coulomb of charge that passes through the cell is the e.m.f. of the cell.

Cells and internal resistance

An electrical cell is made from materials (metal or chemicals, for example). All materials have some resistance. Therefore, a cell must have resistance. This resistance is called the internal resistance of the cell.

A cell can be thought of as a source of e.m.f. with a resistor connected in series.

When currentcurrent: Moving electric charges, for example, electrons moving through a metal wire. flows through the cell a voltage develops across the internal resistance. This voltage is not available to the circuit so it is called the lost volts, (VL).

V_L can also be written as Ir

The voltage across the ends of the cell is called the terminal potential difference, (Vt.p.d).

V_t.p.d can also be written as IR

Because voltage is a measure of energy, and energy is always conserved, the e.m.f. of a cell is equal to the sum of its terminal potential difference, (V_t.p.d), and the lost volts, (V_L).

This gives rise to the equation E = V_t.p.d.+ V_L

This equation can be written in different forms, e.g. E = I (R + r)

Finding the e.m.f. and internal resistance of a cell

To find the e.m.f. and internal resistance of a cell the circuit above is set up.

The variable resistor is altered and readings of potential differences across the terminals of the cell and current through the cell are taken. A graph of these results is then drawn (see above).

At the point at which the line meets the terminal potential difference axis there is no current drawn from the cell. This is called the open circuit potential of the circuit. Because there is no current there will be no lost volts so this value is the e.m.f. of the cell. Where the line meets the terminal potential difference axis is the e.m.f. of the cell.

To find the internal resistance of the cell the gradient of the line is calculated. This has a negative value. The internal resistance of the cell is the same value but without the negative sign. For example, if the slope of the line is -4 then the internal resistance is 4 Ω.

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