An inductor of negligible resistance and inductance 1 H is connected across an AC power supply of 200 V . The frequency of source is 50 Hz. Calculate the value of current passing through it.

Answer

To solve the problem step by step, we will calculate the current passing through the inductor connected to an AC power supply.

### Step 1: Identify the given values
- Inductance (L) = 1 H
- RMS Voltage (Vrms) = 200 V
- Frequency (f) = 50 Hz

### Step 2: Calculate the angular frequency (ω)
The angular frequency (ω) is given by the formula:
\[ \omega = 2\pi f \]
Substituting the given frequency:
\[ \omega = 2\pi \times 50 = 100\pi \, \text{rad/s} \approx 314.16 \, \text{rad/s} \]

### Step 3: Calculate the inductive reactance (Xl)
The inductive reactance (Xl) is calculated using the formula:
\[ X_l = \omega L \]
Substituting the values of ω and L:
\[ X_l = 314.16 \times 1 = 314.16 \, \Omega \]

### Step 4: Calculate the current (Irms)
The current through the inductor can be calculated using Ohm's law for AC circuits:
\[ I_{rms} = \frac{V_{rms}}{X_l} \]
Substituting the values of Vrms and Xl:
\[ I_{rms} = \frac{200}{314.16} \approx 0.6366 \, \text{A} \]

### Step 5: Round off the current value
Rounding off to two decimal places, we get:
\[ I_{rms} \approx 0.64 \, \text{A} \]

### Final Answer
The value of the current passing through the inductor is approximately **0.64 A**.

---