Question

When a battery connected across a resistor of $16\, \Omega$, the 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
$E=12+\frac{12}{16} r \ldots$ (i)
For second case
$E=11+\frac{11}{10} r \ldots$ (ii)
From Eqs. (i) and (ii),
$12+\frac{12}{16} r=11+\frac{11}{10} r$
$\Rightarrow r=\frac{20}{7} \Omega$