Question

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

• A. $80$%
• B. $90$%
• C. $87.5$%
• D. $82.5$%

Answer 1

Answer: (C)

$87.5$%

Power of battery, when charged is given by $P_1=V_1{I}_1$
Electrical energy dissipated is given by $E_1=P_1{t}_1$
$E_1=V_1{I}_1{t}_1=15\times 10\times 8=1200Wh$
Similarly, the electrical energy dissipated during the discharge of battery is given by $E_2=V_2{I}_2{t}_2=14\times 5\times 15=1050Wh$
Hence, watt-hour efficiency of the battery
$\Rightarrow \eta =\frac{E_2}{E_1}\times 100=0.875\times 100=87.5$%