The carrier frequency generated by a tank circuit containing `1 nF` capacitor and `10 muH` inductor is

Options

A. 1592 Hz
B. 1592 kHz
C. 159.2 Hz
D. 15.92 kHz

Answer

To find the carrier frequency generated by a tank circuit containing a capacitor and an inductor, we can use the formula for the resonant frequency \( f \) of an LC circuit:

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

Where:
- \( L \) is the inductance in henries (H)
- \( C \) is the capacitance in farads (F)

### Step 1: Identify the values of \( L \) and \( C \)

Given:
- \( L = 10 \, \mu H = 10 \times 10^{-6} \, H \)
- \( C = 1 \, nF = 1 \times 10^{-9} \, F \)

### Step 2: Substitute the values into the formula

Now we can substitute the values of \( L \) and \( C \) into the formula:

\[ f = \frac{1}{2\pi \sqrt{(10 \times 10^{-6})(1 \times 10^{-9})}} \]

### Step 3: Calculate the product of \( L \) and \( C \)

Calculate \( LC \):

\[ LC = (10 \times 10^{-6}) \times (1 \times 10^{-9}) = 10 \times 10^{-15} = 10^{-5} \times 10^{-9} = 10^{-14} \]

### Step 4: Take the square root of \( LC \)

Now calculate \( \sqrt{LC} \):

\[ \sqrt{LC} = \sqrt{10^{-14}} = 10^{-7} \]

### Step 5: Substitute back into the frequency formula

Now substitute \( \sqrt{LC} \) back into the frequency formula:

\[ f = \frac{1}{2\pi (10^{-7})} \]

### Step 6: Calculate the frequency

Now calculate \( f \):

\[ f = \frac{1}{2\pi} \times 10^{7} \]

Using \( \pi \approx 3.14 \):

\[ f \approx \frac{1}{6.28} \times 10^{7} \approx 15915494.3 \, Hz \approx 1592 \, kHz \]

### Final Answer

Thus, the carrier frequency generated by the tank circuit is approximately:

\[ f \approx 1592 \, kHz \]