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  4. The potential difference in open circuit for a cell is 2.2 volts. When a 4 ohm resistor is connected between its two electrodes the potential difference becomes 2 volts. The internal resistance of the cell will be

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Q. The potential difference in open circuit for a cell is $2.2$ volts. When a $4$ ohm resistor is connected between its two electrodes the potential difference becomes $2$ volts. The internal resistance of the cell will be

Solution:

The potential difference in open circuit for the cell is $2.2$ volts, it means the emf of the battery should be $2.2$ volts.
Now a 4 ohm resistor is connected between its two electrodes, then the potential difference across the battery becomes 2 volts.
$V =\frac{ ER }{ R + r }$
$2=\frac{2.2 \times 4}{4+ r }$
$r =0.4\, \Omega$