`In` an A.C. circuit, a capacitor of `1mu`F value is connected to a source of frequency 1000 rad/sec. The value of capacitive reactance will be –

Options

A. `10 Omega`
B. `100 Omega`
C. `1000 Omega`
D. `10,000 Omega`

Answer

To find the capacitive reactance (Xc) in an AC circuit where a capacitor is connected, we can use the formula:

\[ X_c = \frac{1}{\omega C} \]

where:
- \( \omega \) is the angular frequency (in rad/sec),
- \( C \) is the capacitance (in farads).

### Step-by-step Solution:

1. **Identify the given values**:
- Capacitance \( C = 1 \mu F = 1 \times 10^{-6} F \)
- Angular frequency \( \omega = 1000 \, rad/sec \)

2. **Substitute the values into the formula**:
\[ X_c = \frac{1}{\omega C} = \frac{1}{1000 \times (1 \times 10^{-6})} \]

3. **Calculate the denominator**:
\[ 1000 \times (1 \times 10^{-6}) = 1000 \times 10^{-6} = 10^{-3} \]

4. **Now substitute back into the equation**:
\[ X_c = \frac{1}{10^{-3}} = 10^{3} \]

5. **Convert to ohms**:
\[ X_c = 1000 \, ohm \]

### Final Answer:
The value of the capacitive reactance \( X_c \) is \( 1000 \, ohm \).

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