The circuit connections are made as shown in Figure. With key K open, the emf of cell E is found by connecting a high resistance voltmeter across it.
Since the high resistance voltmeter draws only a very feeble current for deflection, the circuit may be considered as an open circuit. Hence the voltmeter reading gives the emf of the cell. A small value of resistance R is included in the external circuit and key K is closed. The potential difference across R is equal to the potential difference across cell (V).
Fig: Internal resistance of a cell using voltmeter
The potential drop across R, V = IR … (1)
Due to internal resistance r of the cell, the voltmeter reads a value V, less than the emf of cell.
Then V = E – Ir or Ir = E−V … (2)
Dividing equation (2) by equation (1)
Ir/IR = (E-V)/V or, r = (E-V)/V * R
Since E, V and R are known, the internal resistance r of the cell can be determined.