Time constant of an inductive circuit

The correct answer is: A. Increases with increase of inductance and decrease of resistance.

The time constant of an inductive circuit is the time it takes for the current in the circuit to reach 63.2% of its final value after being switched on. It is given by the formula:

$$\tau = \frac{L}{R}$$

where $L$ is the inductance of the circuit and $R$ is the resistance of the circuit.

As you can see from the formula, the time constant is proportional to the inductance and inversely proportional to the resistance. This means that the time constant will increase if the inductance increases and the resistance decreases.

Here is a brief explanation of each option:

• Option A: Increases with increase of inductance and decrease of resistance. This is the correct answer, as explained above.
• Option B: Increases with the increase of inductance and the increase of resistance. This is incorrect, as the time constant will decrease if the resistance increases.
• Option C: Increases with the decrease of inductance and decrease of resistance. This is incorrect, as the time constant will not change if the inductance decreases.
• Option D: Increases with decrease of inductance and increase of resistance. This is incorrect, as the time constant will increase if the inductance decreases.