Calculate the rms value of current passing through a 0.5 `muF ` capacitor connected across an alternating power supply of 220 V. The frequency of power supply in marked 50 Hz.

Answer

To calculate the RMS value of the current passing through a 0.5 µF capacitor connected to an alternating power supply of 220 V with a frequency of 50 Hz, we can follow these steps:

### Step 1: Identify the given values
- Capacitance, \( C = 0.5 \, \mu F = 0.5 \times 10^{-6} \, F \)
- RMS Voltage, \( V_{rms} = 220 \, V \)
- Frequency, \( f = 50 \, Hz \)

### Step 2: Calculate the angular frequency (\( \omega \))
The angular frequency is given by the formula:
\[ \omega = 2 \pi f \]
Substituting the value of \( f \):
\[ \omega = 2 \pi \times 50 \approx 314 \, rad/s \]

### Step 3: Calculate the capacitive reactance (\( X_c \))
The capacitive reactance is given by the formula:
\[ X_c = \frac{1}{\omega C} \]
Substituting the values of \( \omega \) and \( C \):
\[ X_c = \frac{1}{314 \times 0.5 \times 10^{-6}} = \frac{1}{0.000157} \approx 6369.43 \, \Omega \]

### Step 4: Calculate the RMS current (\( I_{rms} \))
The RMS current can be calculated using the formula:
\[ I_{rms} = \frac{V_{rms}}{X_c} \]
Substituting the values of \( V_{rms} \) and \( X_c \):
\[ I_{rms} = \frac{220}{6369.43} \approx 0.0345 \, A \]
This can also be expressed as:
\[ I_{rms} \approx 3.45 \times 10^{-2} \, A \]

### Final Answer
The RMS value of the current passing through the capacitor is approximately \( 0.0345 \, A \) or \( 34.5 \, mA \).

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