Question

The potential difference across the terminals of a battery is $50\text{V},$ when $11\text{A}$ are drawn and $60\text{V}$ when $1\text{A}$ is drawn. The emf and the internal resistance of the battery are

• A. $63\text{V};1\Omega$
• B. $61\text{V};1\Omega$
• C. $62\text{V};2\Omega$
• D. $64\text{V};2\Omega$

Answer 1

The correct option is B $61\text{V};1\Omega$

Since emf of a cell is given by,

$E=V_1+I_{1}r;E=V_2+I_{2}r-----\left(1\right)$

$E=50+11r;E=60+1r-----\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,

$50+11r=60+r$

$(11-1)r=60-50$

$10r=10$

i.e. $r=1\Omega$

From eqn $\left(1\right)E=50+11r$

$=50+11\left(1\right)$

$E=61\text{volt}$