Question

Two identical cells of emf 1.5 V each joined in parallel, supply energy to an external circuit consisting of two resistances of 7 $\Omega$ each joined in parallel. A very high resistance voltmeter reads the terminal voltage of cells to be 1.4 V. Calculate the internal resistance of each cell.

Answer 1

We know that internal resistance of a cell is given by

$r=R(\frac{E}{V}-1)$

Where $R=$ total external resistance ,

$E=$ total emf of cell ,

$V=$ terminal voltage ,

given $E=1.5V,V=1.4V$

now as two given resistances are in parallel therefore total external resistance ,

$R=\frac{7\times 7}{7+7}=\frac{49}{14}\Omega$

therefore $r=\frac{49}{14}(\frac{1.5}{1.4}-1)=0.25\Omega$

$r=$ total internal resistance of the cells,

now the two cells are in parallel therefore internal resistance of each cell ,

$r=\frac{r^{\prime }\times r^{\prime }}{r^{\prime }+r^{\prime }}$

or $0.25=\frac{r^{\prime 2}}{2r^{\prime }}$

or $r^{\prime }=0.50\Omega$