A 30 V storage battery is charged from 120 V direct current supply mains with a resistor being connected in series with battery to limit the charging current to 15 amp. If all the heat produced in circuit, could be made available in heating water, the time it would take to bring 1 kg of water from 15ºC to the 100ºC is.......... minute [Neglect the internal resistance of the battery]
Text Solution
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Sol. As the voltage across the charging battery,
V = E + Ir = 30 + 15 × 0 = 30V
So the potential difference across the resistance
V R = 120 – 30 = 90 V
So the power wasted in heating the circuit
P = VI = 90 × 15 = 1350 W
So the energy wasted as heat in time t
H = P × t = (1350 × t) joule = 
× t calorie
Now if this heat changes the temperature of 1 kg of water from 15ºC to 100ºC
= mc Δθ = 1 × 10 3 × 1 × (100 – 15)
i.e., t = 
= 264.4 s = 4.4 minute
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