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Chapter 20: Problem 2744

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

Expert verified
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

01

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
02

Use the resonant frequency formula

Now, plug in the given values of L and C in the resonant frequency formula: \(f = \frac{1}{2\pi\sqrt{(10\times10^{-6})(1\times10^{-9})}}\)
03

Simplify and solve for 'f'

Let's simplify the formula and solve for 'f': \(f = \frac{1}{2\pi\sqrt{10\times10^{-15}}}\) \(f = \frac{1}{2\pi\sqrt{10^{-14}}}\) \(f = \frac{1}{2\pi\times10^{-7}}\) \(f = \frac{10^{7}}{2\pi}\)
04

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.

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