Question

A coil of resistance \(12 \Omega\) and inductance 18 H is suddenly connected to a dc supply of 30 V. Calculate time constant

• A. 6.7 sec
• B. 4.5 sec
• C. 1.5 sec
• D. 0.11 sec

Hint:

The time constant (\(\tau\)) for an RL circuit is \(\tau = L/R\).
The time constant for an RC circuit is \(\tau = RC\).

Answer 1

The Correct Option is C

For a series RL circuit, the time constant (\(\tau\)) is given by the formula: \[ \tau = \frac{L}{R} \] Where: L = Inductance in Henries (H) R = Resistance in Ohms (\(\Omega\)) Given: Resistance (R) = \(12 \Omega\) Inductance (L) = 18 H The DC supply voltage (30 V) is not needed to calculate the time constant itself. Calculate the time constant: \[ \tau = \frac{18 \text{ H}}{12 \Omega} = \frac{18}{12} \text{ sec} = \frac{3}{2} \text{ sec} = 1.5 \text{ sec} \] The time constant is 1.5 seconds. \[ \boxed{1.5 \text{ sec}} \]