# Internal Resistance

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Internal resistance (r) of any real source is the resistance that charge moving through the material of the source encounters.

The presence of internal resistance in a source of electromotive force means that the potential difference across the terminals of the electrical source (terminal potential difference) is always less than its electromotive force.

By conservation of energy,

Energy delivered by emf source = Energy dissipitated by external resistor + Energy dissipitated by internal resistor

$P_{\epsilon} \, t = P’_{AB} \, t + P_{r} \, t$

$I \epsilon = I V_{AB} + I V_{r}$

$\epsilon = V_{AB} + V_{r}$

$\epsilon = IR + Ir$

$IR = \epsilon \: – Ir$

$V_{AB} = \epsilon \: – Ir$

Terminal potential difference across battery = $\epsilon$ – Ir

Efficiency = $\frac{P_{load}}{P_{emf}}$ = $\frac{I^{2}R}{I \epsilon}$ = $\frac{IR}{I (R + r)}$ = $\frac{R}{R +r}$

### 5 thoughts on “Internal Resistance”

1. Thanks for the prompt reply. So if a voltmeter was connected across the circuit from A to B, the figure it would show would be the TPD?

• Sorry for the late reply.

Yes, it would be.

• No worries, thanks for the reply.

2. Hello, firstly thanks a ton for this wonderful website.
I don’t think i quite understand what Terminal Potential Difference is. I can see that TPD=IR. So is TPD just the total voltage across the circuit?

• Terminal potential difference is the potential difference across the cell. For a non-ideal cell, there will be internal resistance in the cell. Hence, terminal potential difference will be the emf – potential across the internal resistance.

TPD is just the potential difference across point A and B in the diagram above.