Question

When a battery connected across a resistor of $16 \,\Omega$, voltage across the resistor is $12\, V$. When the same battery is connected across a resistor of $10 \,\Omega$, voltage across it is $11\, V$. The internal resistance of the battery (in ohm) is

• A. $ \frac{10}{7} $
• B. $ \frac{20}{7} $
• C. $ \frac{25}{7} $
• D. $ \frac{30}{7} $

Answer 1

Answer: (B)

Here, $V < E$
$\therefore \, E=V+I r $
For first case,
$E=12+\frac{12}{16} r \, ...(i)$
For second case,
$E=11+\frac{11}{10} r\,...(ii)$
From Eqs. (i) and (ii), we get
$12+\frac{12}{16} r =11+\frac{11}{100} r $
$\Rightarrow \,r =\frac{20}{7} \,\Omega $