**Series Circuit**

R_{Total} = R_{1} + R_{2} + R_{3} + ... + R_{n}

**Parallel Circuit**

^{1}/R_{Total} = ^{1}/R_{1} + ^{1}/R_{2} + ^{1}/R_{3} + ... + ^{1}/R_{N}

The total resistance is always less than the smallest value of resistance.

**Internal Resistance**

A cell in a circuit has its own internal resistance, *r*. The greater the cell’s current the more work is done against the cell’s internal resistance, and therefore less can be done on the external circuit.

emf = terminal p.d. + p.d. across internal resistance

E = V + Ir

**Variable Resistors**

A variable resistor allows for finer control over the amount of resistance.

It could be a mechanism which changes the length of wire through which current must flow, as seen in the example below:

**Energy Transfer and Power**

Resisters heat up as current passes through them. The energy transferred by heating can be found by the following:

ΔE = V I Δt (Energy equals Voltage x Current x Time)

Power is the rate of working or rate of energy transfer.

P = I V (Power = Current x Voltage).

Given the resistance equation we can work out:

P = I^{2}R