Q115 / 120 · VITEEE 2014 · Physics

A battery is charged at a potential of $15 \mathrm{~V}$ in $8 \mathrm{~h}$ when the current flowing is $10 \mathrm{~A}$. The battery on discharge supplies a current of $5 \mathrm{~A}$ for $15 \mathrm{~h}$. The mean terminal voltage during discharge is $14 \mathrm{~V}$. The watt-hour efficiency of battery is

  • A
    $80 \%$
  • B
    $90 \%$
  • Correct answer
    C
    $87.5 \%$
  • D
    $82.5 \%$

Solution

Power of battery, when charged is given by $\mathrm{P}_{1}=\mathrm{V}_{1} \mathrm{I}_{1}$ Electrical energy dissipated id given by $\begin{array}{l} \mathrm{E}_{1}=\mathrm{P}_{1} \mathrm{t}_{1} \\ \mathrm{E}_{1}=\mathrm{V}_{1} \mathrm{I}_{1} \mathrm{t}_{1}=15 \times 10 \times 8=1200 \mathrm{Wh} \end{array}$ Similarly, the electrical energy dissipated during the discharge of battery is given by $\begin{array}{l} \mathrm{E}_{2}=\mathrm{V}_{2} \mathrm{I}_{2} \mathrm{t}_{2} \\ =14 \times 5 \times 15=1050 \mathrm{Wh} \end{array}$ Hence, watt-hour efficiency of the battery $\Rightarrow \eta=\frac{E_{2}}{E_{1}} \times 1000.875 \times 100=87.5 \%$

Hence, the correct answer is option: 'C'.

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