A 220V, 50 Hz ac source is connected to a series combination of a 3.16 micro farad capacitor , 0.63 H inductor and 600 ohm resistor.
Reactance of the capacitor is

Answer

To find the reactance of the capacitor in the given circuit, we can follow these steps:

### Step 1: Identify the given values
- Voltage (V) = 220V (not needed for reactance calculation)
- Frequency (f) = 50 Hz
- Capacitance (C) = 3.16 µF = 3.16 × 10^(-6) F

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

### Step 3: Calculate the reactance of the capacitor (XC)
The reactance of the capacitor (XC) is given by the formula:
\[ X_C = \frac{1}{\omega C} \]
Substituting the values of ω and C:
\[ X_C = \frac{1}{100\pi \times 3.16 \times 10^{-6}} \]

### Step 4: Simplify the expression
Calculating the denominator:
\[ 100\pi \times 3.16 \times 10^{-6} \approx 100 \times 3.14 \times 3.16 \times 10^{-6} \approx 9.87 \times 10^{-4} \]
Thus:
\[ X_C = \frac{1}{9.87 \times 10^{-4}} \approx 1013.3 \text{ ohms} \]

### Step 5: Final calculation
Using a calculator to find:
\[ X_C \approx 1007.30 \text{ ohms} \]

### Conclusion
The reactance of the capacitor is approximately:
\[ X_C \approx 1007.30 \text{ ohms} \]

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