Internal Resistance

Explanation

All electrical cells have some amount of resistance inside of them - whether unintentionally, due to the natural resistance of the materials the cell is made out of, or intentionally, for safety reasons in certain high-voltage applications. This is known as internal resistance.

The symbol for internal resistance is $r$ .

Don't get your Rs mixed up!

$r$ (lowercase) is for internal resistance.
$R$ (uppercase) is for load resistance.

Electromotive Force

The electromotive force (EMF) of a circuit is the energy transferred into the circuit per unit of charge. It is equal to the voltage across a cell, excluding the internal resistance.

Since EMF is a voltage, we can use the voltage formula, $W = Q V$ .

Terminal Potential Difference

The terminal potential difference, or terminal voltage, is the voltage across the entire power supply, including its internal resistance. This is also equal to the potential difference across the load - since both form identical circuits!

Lost Volts

The actual productive voltage of a power supply with internal resistance will be lower than its EMF, because some voltage is lost on the internal resistance. This lost voltage is known as lost volts.

Since the ratio of voltage across components in a series circuit is equal to the ratio of the components' respective resistance (as it is a potential divider circuit), the greater the resistance of the load, the less the lost volts are.

Formula

E = V + I r

Variable Key

$E$ is the EMF, in volts.
$V$ is the terminal p.d., in volts.
$I$ is the current through the circuit, in amperes.
$r$ is the internal resistance of the power supply.