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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?
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Solution
Given: Emf of the battery, E = 10 V
The 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 = `E/(R + r)`
R + r = `E/I`
`R + 3 = 10/0.5`
R + 3 = 20
∴ R = 20 − 3
= 17 Ω
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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