Question

The time constant of L-R circuit is

• A. \(LR\)
• B. \(\dfrac{L}{R}\)
• C. \(\dfrac{R}{L}\)
• D. \(\dfrac{1}{LR}\)

Hint:

Remember: in an L-R circuit, \(\tau = L/R\) (analogous to \(\tau = RC\) in a capacitive circuit). The inductor opposes change in current.

Answer 1

The Correct Option is B

Step 1: Underlying Concept:
Time constant \(\tau\) of an L-R circuit: time for current to reach about 63% of final value. Step 2: Explanation:
Current growth equation: \(I = I_0(1 - e^{-Rt/L})\). For exponent to be dimensionless: \(\frac{Rt}{L} \Rightarrow \tau = \frac{L}{R}\). Hence, \(\tau\) has dimensions of time \([T]\). Step 3: Conclusion:
\[ \boxed{\tau = \frac{L}{R}} \]