Question

Tank Circuit Contains 1 nf capacitor and 10 microhenry inductor What is the carrier frequency generated by it? (A) \(1629 \mathrm{KHz}\) (B) \(1592 \mathrm{KHz}\) (C) \(1582 \mathrm{MHz}\) (D) \(156.2 \mathrm{KHz}\)

Short answer

The carrier frequency generated by the tank circuit is approximately 1591.55 KHz. Therefore, the closest answer is (B) 1592 KHz.

Step-by-step solution

Convert the given values

Convert the given capacitance and inductance values to base units (Farad and Henry, respectively). Capacitance (C) = 1 nF = \(1\times10^{-9}\) F Inductance (L) = 10 µH = \(10\times10^{-6}\) H

Use the resonant frequency formula

Now, plug in the given values of L and C in the resonant frequency formula: \(f = \frac{1}{2\pi\sqrt{(10\times10^{-6})(1\times10^{-9})}}\)

Simplify and solve for 'f'

Let's simplify the formula and solve for 'f': \(f = \frac{1}{2\pi\sqrt{10\times10^{-15}}}\) \(f = \frac{1}{2\pi\sqrt{10^{-14}}}\) \(f = \frac{1}{2\pi\times10^{-7}}\) \(f = \frac{10^{7}}{2\pi}\)

Calculate the carrier frequency

Now, calculate the carrier frequency: \(f = \frac{10^{7}}{2\pi} \approx 1591549.43 \, \mathrm{Hz}\) To convert Hz to KHz, divide by 1000: \(f= \frac{1591549.43 \, \mathrm{Hz}}{1000} \approx 1591.55 \, \mathrm{KHz}\) So, the carrier frequency generated is approximately 1591.55 KHz. Based on the given options, the closest answer is: (B) 1592 KHz.