Question

The potential difference across the terminals of a battery is $8.4\text{V}$ when there is a current of $1.5\text{A}$ in the battery from the negative to the positive terminal. When the current is $3.5\text{A}$ in the reverse direction, the potential difference becomes $9.4\text{V}$.
$\left(a\right)$ What is the internal resistance of the battery?
$\left(b\right)$ What is the EMF of the battery ?

• A. $0.2\Omega$, $5.2\text{V}$
• B. $0.2\Omega$, $8.7\text{V}$
• C. $0.4\Omega$, $5.2\text{V}$
• D. $0.4\Omega$, $8.7\text{V}$

Answer 1

The correct option is B $0.2\Omega$, $8.7\text{V}$

If $i$ is the current supplied by a battery having internal resistance $r$, the terminal voltage is given by, $$V=E-ir$$As per the given condition,

$8.4=E-1.5r.......\left(1\right)$

$9.4=E+3.5r.......\left(2\right)$

Subtracting equation $\left(1\right)$ from $\left(2\right)$,

$\Rightarrow 1=5r$

$\therefore r=0.2\Omega$

Substituting $r$ in any one of the above equation we get,

$E=8.7\text{V}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option (b) is the correct answer.