Q113 / 180 · JIPMER 2019 · Physics
For a battery the electromotive force is 1.5 V . Terminal voltage is 1.25 V . Power supplied to external resistance is 2.5 W . Find the internal resistance of battery.
- Correct answerA$0.125 \Omega$
- B$0.25 \Omega$
- C$0.5 \Omega$
- D$0.1 \Omega$
Solution
EMF of battery, $\mathrm{E}=1.5 \mathrm{~V}$
Terminal voltage, $\mathrm{V}=1.25 \mathrm{~V}$
Power supplied to external resistance (R),
i.e.
$\begin{aligned}
\mathrm{P} & =2.5 \mathrm{~W} \\
\mathrm{P} & =\frac{\mathrm{V}^2}{\mathrm{R}} \\
2.5 & =\frac{(1.25)^2}{\mathrm{R}}
\end{aligned}$
$\begin{array}{ll}
\Rightarrow & \mathrm{R}=\frac{1.25 \times 1.25}{2.5} \\
\Rightarrow & \mathrm{R}=0.625 \Omega
\end{array}$
When battery is used to supply the power to load resistance, then $\mathrm{V}=\mathrm{E}-\mathrm{Ir}$
$\begin{aligned}
\Rightarrow V & =E-\left(\frac{V}{R}\right) \cdot r \Rightarrow r=\left(\frac{E}{V}-1\right) R=\left(\frac{1.5}{1.25}-1\right) 0.625 \\
& =0.125 \Omega
\end{aligned}$
Hence, the correct answer is option: 'A'.