Question

The current in an \( L-R \) circuit builds up to \( 3/4 \) of its steady state value in 4 seconds. The time constant of this circuit is

• A. \( \frac{1}{3} \) sec
• B. \( \frac{2}{3} \) sec
• C. \( \ln 2 \) sec
• D. \( \ln 3 \) sec

Hint:

In an \( L-R \) circuit, the time constant is the time taken for the current to reach about 63% of its steady-state value.

Answer 1

The Correct Option is B

Step 1: Time Constant in \( L-R \) Circuit.
The time constant \( \tau \) of an \( L-R \) circuit is given by: \[ \tau = \frac{L}{R} \] The current reaches \( 3/4 \) of its steady state value in 4 seconds, which is approximately the time constant \( \tau \). Thus, the time constant is \( \tau = \frac{2}{3} \) seconds.
Step 2: Conclusion.
The correct answer is (B), \( \frac{2}{3} \) sec.