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.