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Chapter 28: Problem 28

Your university's FM station broadcasts at \(89.5 \mathrm{MHz}\). The \(L C\) circuit that establishes this frequency has a 47 -pF capacitor. What's the corresponding inductance?

Short Answer

Expert verified
The inductance \(L\) of the circuit is approximately \(0.006\) H.

Step by step solution

01

Convert Megahertz to Hertz

Convert the given frequency of 89.5 MHz to hertz by multiplying with \(10^6\). The frequency \(f\) is therefore \(89.5 \times 10^6\) Hz.
02

Convert Picofarad to Farad

Convert the given capacitance of 47 pF to farad by multiplying with \(10^{-12}\). So capacitance \(C\) is \(47 \times 10^{-12}\) F.
03

Rearrange the resonance frequency formula

Rearrange the resonance frequency formula to solve for \(L\): \(L = 1 / (4 \pi^2 f^2 C)\).
04

Substitute the values

Substitute the frequency and capacitance values into the rearranged formula: \(L = 1 / (4 \pi^2 (89.5 \times 10^6)^2 \times (47 \times 10^{-12}))\).
05

Calculate

Calculate the above expression to find the corresponding inductance \(L\).

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Most popular questions from this chapter

A series \(R L C\) circuit has power factor 0.80 and impedance \(100 \Omega\) at \(60 \mathrm{Hz}\). (a) What's the resistance? (b) If the inductance is \(0.10 \mathrm{H},\) what's the resonant frequency?

An inductor and capacitor are connected in series across an AC generator, and the voltage across the inductor is higher than across the capacitor. Is the generator frequency above or below resonance?

A power supply like that of Fig. 28.23 is supposed to deliver 22-V DC at a maximum current of 150 mA. The transformer's peak output voltage can charge the capacitor to a full \(22 \mathrm{V},\) and the primary is supplied with \(60-\mathrm{Hz}\) AC. What capacitance will ensure that the output voltage stays within \(3 \%\) of the rated \(22 \mathrm{V} ?\)

Two capacitors are connected in parallel across a \(10-\mathrm{V}\) rms, \(10-\mathrm{kHz}\) sine-wave generator, and the generator supplies a total rms current of 30 mA. With capacitors rewired in series, the rms generator current drops to 5.5 mA. Find the two capacitances.

An electric drill draws \(4.6 \mathrm{A}\) rms at \(120 \mathrm{V}\) rms. If the current lags the voltage by \(25^{\circ},\) what's the drill's power consumption?
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