Question

A solenoid has an inductance of 60 H and a resistance of 30 ohm. If it is connected to a 100 V battery, how long will it take for the current to reach \( e^{-1} \) of its maximum value?

• A. 1 s
• B. 2 s
• C. e second
• D. 2 e second

Hint:

The time constant \( \tau \) in an RL circuit defines the time required for the current to reach approximately 63.2% of its maximum value.

Answer 1

The Correct Option is B

Step 1: Understand the RL circuit time constant.
For an RL circuit, the current \( I \) as a function of time is given by: \[ I(t) = I_{\text{max}} \left( 1 - e^{-\frac{t}{\tau}} \right) \] where \( \tau = \frac{L}{R} \) is the time constant, \( L \) is the inductance, and \( R \) is the resistance.

Step 2: Calculate the time constant.
Given \( L = 60 \, \text{H} \) and \( R = 30 \, \Omega \), the time constant is: \[ \tau = \frac{L}{R} = \frac{60}{30} = 2 \, \text{seconds} \]

Step 3: Time for current to reach \( e^{-1} \) of its maximum value.
At \( t = \tau \), the current reaches \( e^{-1} \) of its maximum value, so the time required is \( 2 \, \text{seconds} \).

Step 4: Conclusion.
The time required for the current to reach \( e^{-1} \) of its maximum value is 2 seconds, which is option (2).