In LCR circuit, L = 1H, R = `10Omega`, C = 1 `muF`., the resonant frequency is: (in Hz)

Options

A. `(500)/pi`
B. `250pi`
C. `500pi`
D. None of these

Explanation

To find the resonant frequency of an LCR circuit, we can use the formula for resonant frequency \( f \):

\[ f = \frac{1}{2\pi \sqrt{LC}} \]

**Step 1: Identify the values of L and C.**
- Given:
- Inductance \( L = 1 \, \text{H} \)
- Capacitance \( C = 1 \, \mu\text{F} = 1 \times 10^{-6} \, \text{F} \)

**Step 2: Substitute the values into the formula.**
\[ f = \frac{1}{2\pi \sqrt{1 \times (1 \times 10^{-6})}} \]

**Step 3: Simplify the expression inside the square root.**
\[ \sqrt{1 \times 10^{-6}} = \sqrt{10^{-6}} = 10^{-3} \]

**Step 4: Substitute the simplified value back into the frequency formula.**
\[ f = \frac{1}{2\pi \times 10^{-3}} \]

**Step 5: Simplify the fraction.**
\[ f = \frac{1}{2\pi} \times 10^{3} = \frac{1000}{2\pi} \]

**Step 6: Further simplify the fraction.**
\[ f = \frac{500}{\pi} \, \text{Hz} \]

Thus, the resonant frequency of the LCR circuit is:
\[ \boxed{\frac{500}{\pi} \, \text{Hz}} \]