Question Detail
Question
When a battery, a resistor, a switch, and an inductor form a circuit, and the switch is closed, the inductor acts to oppose the change in the current. How is the time constant of the inductor affected by doubling the resistance in the circuit?
Correct Answer
Option D is the correct answer.
Detailed Explanation
The time constant (τ) for an RL (Resistor-Inductor) circuit is given by the formula τ = L/R, where L is the inductance and R is the resistance.If the resistance (R) is doubled, the new resistance becomes 2R.The new time constant (τ') would be L/(2R).So, τ' = (1/2) * (L/R) = (1/2) * τ.Therefore, the time constant would decrease to one-half its original value.
Hint
Remember the formula for the time constant of an RL circuit.