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

Question

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

TestHub · Accepted Answer

The power of the battery, when charged is given by

$P_{1} = V_{1} I_{1}$

The electrical energy dissipated is given by

$E_{t} = P_{1} t_{1}$

$E_{1} = V_{1} I_{1} T_{1} = 15 \times 10 \times 8$

$= 1200 Wh$

Similarly, the electrical energy dissipated during the discharge of battery is given by

$E_{2} = V_{2} I_{2} t_{2}$

$= 14 \times 5 \times 15$

$= 1050 Wh$

Hence, watt-hour efficiency of the battery is given by

$η = \frac{E_{2}}{E_{1}} \times 100$

$= 0.875 \times 100 = 87.5 %$

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