## 2010-01-18

### Analyzing Electromotive Force and Internal Resistance

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Before explaining further, I would like to make a light bulb and a cell as an analogy.

1. The cell functions as the source of energy and the light bulb is the energy consuming device.
2. The light bulb converts electrical energy into heat and light energy.
3. The electrical charges that flow round the circuit transfer energy from the source (the cell) to the device.

4. In a cell, chemical reaction converts chemical energy into electrical energy. This energy pushes the free electrons to move them from the negative terminal to the positive terminal of the cell.

5. Work done by the source in driving the charges around a complete circuit. This work done is known as electromotive force.

6. The electromotive force (e.m.f.) is the work done by one source in driving a unit charge around a complete circuit. <-------------- i="">need to remember this term

Electromotive Force and Potential Difference

1. The definition for electromotive force (e.m.f.) is similar to that of potential difference (p.d.). However, there is a distinction between e.m.f. and p.d.

2. The e.m.f. of a cell is the energy supplied to a unit of charge within the cell.

3. The p.d. across a component in a circuit is the conversion of electrical energy into others forms of energy when a unit of charge passes through the components.

Internal Resistance

1. In an open circuit when there is no current flow, the potential difference, V across the cell is the electromotive force, E of the cell.

2. In a closed circuit when there is a current flow, the potential difference, V across the cell is smaller than the electromotive force, E of the cell.

3. This drop in potential difference across the cell is caused by the internal resistance of the cell.

4. The internal resistance of a source or a cell is the resistance against the moving charge due to the electrolyte in a source or the cell.

5. Work is needed to drive a charge against the internal resistance.

6. This causes a drop in potential difference across the cell as the charge flows through it.

Electromotive force and Internal Resistance

1. A cell can be modeled as an e.m.f., E connected in series with an internal resistor, r.

2. When a high resistance voltmeter is connected across the terminals of the cell, the reading of the voltmeter gives the e.m.f., E of the cell.

3. If a resistor, R is then connected to the terminals of the cell, the voltmeter reading is the potential difference, V across the terminals of the cell.

4. The value of potential difference, V is less than e.m.f. of the cell. The difference between E and V is due to the potential difference needed to drive the current, I through the internal resistor, r of the cell.
Hence,

E-V = Ir ═> E = V + Ir

5. The internal resistance, r is given by:

r = E-V / I