An inductor of inductance 5 H is connected across an alternating power supply of 220 volts . The frequency of source is 50 Hz. Calculate the maximum value of curent in the inductor .

Answer

To solve the problem of finding the maximum value of current in an inductor connected to an alternating power supply, we will follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Inductance (L) = 5 H
- RMS Voltage (Vrms) = 220 V
- Frequency (f) = 50 Hz

2. **Calculate Angular Frequency (ω):**
The angular frequency (ω) is given by the formula:
\[ \omega = 2 \pi f \]
Substituting the value of frequency:
\[ \omega = 2 \pi \times 50 = 314 \, \text{rad/s} \]

3. **Calculate Inductive Reactance (XL):**
The inductive reactance (XL) is calculated using the formula:
\[ X_L = L \omega \]
Substituting the values of L and ω:
\[ X_L = 5 \times 314 = 1570 \, \Omega \]

4. **Calculate RMS Current (Irms):**
The RMS current (Irms) can be calculated using Ohm's law for AC circuits:
\[ I_{rms} = \frac{V_{rms}}{X_L} \]
Substituting the values:
\[ I_{rms} = \frac{220}{1570} \approx 0.14 \, \text{A} \]

5. **Calculate Maximum Current (I0):**
The maximum current (I0) is related to the RMS current by the formula:
\[ I_0 = I_{rms} \times \sqrt{2} \]
Substituting the value of Irms:
\[ I_0 = 0.14 \times \sqrt{2} \approx 0.14 \times 1.414 \approx 0.198 \, \text{A} \]

6. **Final Result:**
The maximum value of current (I0) in the inductor is approximately:
\[ I_0 \approx 0.2 \, \text{A} \]