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?

Answer 1

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,
\(I = \frac{E}{R+r}\)
\(R+r = \frac{E}{I}\)
\(R+r = \frac{10}{0.5}\)
\(R+r = 20 Ω\)
\(∴ R = 20-3 = 17 Ω\)
Terminal voltage of the resistor = V
According to Ohm’s law,
\(V = IR\)
\(V = 0.5 × 17\)
\(V = 8.5 V\)
Therefore, the resistance of the resistor is 17 Ω and the terminal voltage is 8.5 V.