**Question:**

A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

**Solution:**

Emf of the battery, *E* = 10 V

Internal resistance of the battery, *r* = 3 Ω

Current in the circuit, *I* = 0.5 A

Resistance of the resistor = *R*

The relation for current using Ohm’s law is,

$I=\frac{E}{R+r}$

$R+r=\frac{E}{I}$

$=\frac{10}{0.5}=20 \Omega$

$\therefore R=20-3=17 \Omega$

Terminal voltage of the resistor = *V*

According to Ohm’s law,

*V* = *IR*

= 0.5 × 17

= 8.5 V

Therefore, the resistance of the resistor is 17 Ω and the terminal voltage is

8.5 V.

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