Question

When a battery connected across a resistor of $15$ $\Omega$, voltage across the resistor in $12$ $V$. 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. $\frac{2}{7}$
• D. $\frac{30}{7}$

Answer 1

The correct option is B $\frac{20}{7}$

$\frac{E\cdot 16}{16+R}=12$ (equation $01$)

$\frac{E\cdot 10}{10+R}=11$ (equation $02$)

$\Rightarrow \frac{16}{10}=\frac{12(16+R)}{11(10+R)}$

$\Rightarrow 16\times 11(10+R)=120(16+R)$

$\Rightarrow 1760+176R=1920+120R$

$\Rightarrow 56R=160$

$\Rightarrow R=\frac{160}{56}=\frac{20}{7}$ $\Omega$