3.11 A storage battery of emf 8.0 V and internal resistance 0.5 Ω is being charged by a 120 V dc supply using a series resistor of 15.5 Ω. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

Given,

Emf of battery, E = 8 V

Internal resistance of battery, r = 0.5 Ω

Supply Voltage, V = 120 V

The resistance of the resistor, R = 15.5 Ω

Let V' be the effective voltage in the circuit.

Now, V' = V - E

V' = 120 - 8  = 112 V

Now, Current flowing in the circuit is:

I = V' / (R + r)

$\implies I = \frac{112}{15.5 + 0.5} = 7 A$

Now, Using Ohm ’s Law:

Voltage across resistor R is v = IR

v = 7 x 15.5 = 108.5 V

Now, Voltage supplied, V = Terminal Voltage of battery + v

$\therefore$ Terminal Voltage of battery = 120 -108.5  = 11.5 V

The purpose of having a series resistor is to limit the current drawn from the supply.

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