Time constant of circuit containing pure inductor connected across the alternating voltage is ………… .

Answer

To determine the time constant of a circuit containing a pure inductor connected across an alternating voltage, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Time Constant**:
The time constant (τ) in an electrical circuit is a measure of the time it takes for the current to reach approximately 63.2% of its final steady-state value after a change in voltage. It is defined as the ratio of inductance (L) to resistance (R):
\[ \tau = \frac{L}{R} \]

2. **Identifying the Components**:
In this case, we are dealing with a pure inductor. A pure inductor is characterized by having inductance (L) but no resistance (R).

3. **Setting Resistance to Zero**:
For a pure inductor, the resistance (R) is considered to be zero. Therefore, we substitute R = 0 into the time constant formula:
\[ \tau = \frac{L}{0} \]

4. **Calculating the Time Constant**:
Since division by zero is undefined, we can conclude that the time constant for a pure inductor is infinite. This means that the current will never reach a steady state in a pure inductor circuit connected to an alternating voltage.

5. **Conclusion**:
Thus, the time constant of a circuit containing a pure inductor connected across an alternating voltage is infinite.

### Final Answer:
The time constant of a circuit containing a pure inductor connected across alternating voltage is infinite.

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