For a battery the electromotive force is 1.5 V . Terminal voltage...

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.

Options

A $0.125 \Omega$
B $0.25 \Omega$
C $0.5 \Omega$
D $0.1 \Omega$

Correct answer

A. $0.125 \Omega$

Step-by-step 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}

Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction