A 2`muF ` capacitor is connected across an AC power supply . Calculate the frequency of the supply if the capacitive reactance of the capacitor is 10 `Omega` .

Answer

To solve the problem, we need to find the frequency of an AC power supply connected to a capacitor with a given capacitive reactance. Here are the steps to calculate the frequency:

### Step-by-Step Solution:

1. **Identify the given values:**
- Capacitance, \( C = 2 \mu F = 2 \times 10^{-6} F \)
- Capacitive reactance, \( X_c = 10 \Omega \)

2. **Use the formula for capacitive reactance:**
The formula for capacitive reactance is given by:
\[ X_c = \frac{1}{2 \pi f C} \]
where \( f \) is the frequency in hertz.

3. **Rearrange the formula to solve for frequency \( f \):**
We can rearrange the formula to find \( f \):
\[ f = \frac{1}{2 \pi X_c C} \]

4. **Substitute the known values into the equation:**
Now, substitute \( X_c = 10 \Omega \) and \( C = 2 \times 10^{-6} F \):
\[ f = \frac{1}{2 \pi (10) (2 \times 10^{-6})} \]

5. **Calculate \( 2 \pi \):**
Using \( \pi \approx 3.14 \):
\[ 2 \pi \approx 6.28 \]

6. **Calculate the denominator:**
\[ 2 \pi (10) (2 \times 10^{-6}) = 6.28 \times 10 \times 2 \times 10^{-6} = 6.28 \times 20 \times 10^{-6} = 125.6 \times 10^{-6} \]

7. **Calculate the frequency \( f \):**
Now, plug this value back into the frequency formula:
\[ f = \frac{1}{125.6 \times 10^{-6}} \approx 7961.78 \text{ Hz} \]

### Final Answer:
The frequency of the AC power supply is approximately \( 7961.78 \text{ Hz} \).