Question

A coil of 40 henry inductance is connected in series with a resistance of 8 ohms and the combination is joined to the terminals of a 2-volt battery. The time constant of the circuit is

• A. \(\frac{1}{5}\) seconds
• B. 40 seconds
• C. 20 seconds
• D. 5 seconds

Answer 1

The Correct Option is D

To solve this problem, we need to determine the time constant of the given RL (Resistor-Inductor) circuit. The time constant (\( \tau \)) of an RL circuit is given by the formula:

\(\tau = \frac{L}{R}\)

where \(L\) is the inductance and \(R\) is the resistance.

Given values:

• Inductance, \(L = 40 \, \text{henry}\)
• Resistance, \(R = 8 \, \text{ohms}\)

Substituting these values into the formula to calculate the time constant:

\[ \tau = \frac{L}{R} = \frac{40}{8} = 5 \, \text{seconds} \]

Thus, the time constant of the circuit is 5 seconds.

Conclusion: The correct answer is 5 seconds.

This solution confirms the choice from the provided options.