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Chapter 28: Problem 63

A series \(R L C\) circuit with \(R=1.3 \Omega, L=27 \mathrm{mH},\) and \(C=\) \(0.33 \mu \mathrm{F}\) is connected across a sine-wave generator. If the capacitor's peak voltage rating is \(600 \mathrm{V},\) what's the maximum safe value for the generator's peak output voltage when it's tuned to resonance?

Short Answer

Expert verified
The maximum safe value for generator's peak output voltage is \(600 \, V\).

Step by step solution

01

Find the peak current

The maximum safe current through the circuit is determined by the peak voltage rating of the capacitor and the impedance of the circuit at resonance, which is equal to the resistance. Use Ohm's Law, \(I = V/R\), where \(I\) is the current, \(V\) is the voltage, and \(R\) is the resistance. The maximum safe current is therefore \(I = 600/1.3 = 461.54 \, A\).
02

Determine the generator’s peak output voltage

The peak voltage across the circuit (which will be the generator's peak output voltage) is the product of the peak current and the total impedance at resonance, which equals the resistance. Again applying Ohm's Law, \(V = I*R\), calculate the generator's peak voltage as: \(V = 461.54*1.3 = 600 \, V\).

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Most popular questions from this chapter

Find the reactance of a \(3.3-\mu \mathrm{F}\) capacitor at (a) \(60 \mathrm{Hz},\) (b) \(1.0 \mathrm{kHz}\) and (c) \(20 \mathrm{kHz}\)

An industrial electric motor runs at \(208 \mathrm{V}\) rms and \(400 \mathrm{Hz}\). What are (a) the peak voltage and (b) the angular frequency?

You're concerned about a circuit that will be used in a remote communications installation. The series RLC circuit with \(R=5.5 \Omega, L=180 \mathrm{mH},\) and \(C=0.12 \mu \mathrm{F}\) is connected across a sine-wave generator. The inductor can safely handle 1.5 A of current. The peak generator output when it's tuned to resonance will be \(8.0 \mathrm{V} .\) Will the inductor current stay within a safe limit?

An LC circuit includes a \(0.025-\mu \mathrm{F}\) capacitor and a \(340-\mu \mathrm{H}\) inductor. (a) If the peak capacitor voltage is \(190 \mathrm{V},\) what's the peak inductor current? (b) How long after the voltage peak does the current peak occur?

Why does it make sense that inductive reactance increases with frequency?
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