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(i) A storage battery of emf 8V, interna...

(i) A storage battery of emf `8V`, internal resistance `1 Omega` is being charged by a `120 V` d.c. source using a `15 Omega` resistor in series in the circuit. Calculate the current in the circuit (ii) terminal voltage across the battery during charging and (ii) chemical energy stored in the battery in `5` minutes.

Text Solution

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Here, e.m.f. of the battery = 8.0 V , Voltage of d.c. supply = 120 V
Internal resistance of battery, `r = 0.5 Omega`, External resistance, `R = 15.5 Omega`
Since a storage battery of e.m.f. 8 V is charged with d.c. supply of 120 V, the effective e.m.f. in the circuit is given by `epsilon = 120 -8 = 112V`
Total resistance of the circuit `= R + r = 15.5 + 0.5= 16.0 Omega`
`:.` Current in the circuit during charging is given by, `I = epsilon/R+r = 112/16 = 7.0A`
`:.` Voltage across R = `IR = 7.0 xx 15.5 = 108.5V`
During charging, the voltage of the d.c. supply in a circuit must be equal to the sum of the voltage drop across R and terminal voltage of the battery
`:. 120 = 108.5 + V or V = 120-108.5 = 11.5 V`
The series resistor limits the current drawn from the external source of d.c. supply. In its absence the currnet will be dangerously high.
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