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Chapter 28: Problem 21

A 15 - \(\mu\) F capacitor carries \(1.4 \mathrm{A}\) rms. What's its minimum safe voltage rating if the frequency is (a) \(60 \mathrm{Hz}\) and (b) \(1.0 \mathrm{kHz} ?\)

Short Answer

Expert verified
The minimum safe voltage rating of the capacitor when the frequency is 60Hz is equal to \(V1\) volts and when the frequency is 1kHz, it is equal to \(V2\) volts. The final safe voltage rating should be higher than both \(V1\) and \(V2\).

Step by step solution

01

Calculate reactance for 60Hz

Find the capacitive reactance at 60Hz using the formula: \(Xc1 = 1 / (2 * 蟺 * 60 Hz * 15 碌F)\)
02

Calculate voltage for 60Hz

Calculate the voltage at 60Hz using Ohm's law \(V1 = 1.4A * Xc1\)
03

Calculate reactance for 1 kHz

Find the capacitive reactance at 1 kHz using the formula: \(Xc2 = 1 / (2 * 蟺 * 1 kHz * 15 碌F)\)
04

Calculate voltage for 1 kHz

Calculate the voltage at 1kHz using Ohm's law \(V2 = 1.4A * Xc2\)
05

Determine the minimum safe voltage

The minimum safe voltage rating should be higher than both V1 and V2

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Most popular questions from this chapter

An AC current is given by \(I=495 \sin (9.43 t),\) with \(I\) in \(\mathrm{mA}\) and \(t\) in ms. Find (a) the rms current and (b) the frequency in Hz.

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

A 2.0 - \(\mu\) F capacitor has 1.0 -k \(\Omega\) reactance. (a) What's the frequency of the applied voltage? (b) What inductance would give the same reactance at this frequency? (c) How would the reactances compare if the frequency were doubled?

A 2.2 -nF capacitor and one of unknown capacitance are in parallel across a \(10-\mathrm{V}\) rms sine-wave generator. At \(1.0 \mathrm{kHz}\) the generator supplies a total current of \(3.4 \mathrm{mA}\) rms. The generator frequency is then decreased until the rms current drops to 1.2 mA. Find (a) the unknown capacitance and (b) the lower frequency.

A series \(R L C\) circuit has \(R=18 \mathrm{k} \Omega, C=14 \mu \mathrm{F},\) and \(L=0.20 \mathrm{H}\) (a) At what frequency is its impedance lowest? (b) What's the impedance at this frequency?
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