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Chapter 28: Problem 18

Find the rms current in a \(1.0-\mu \mathrm{F}\) capacitor connected across \(120-\mathrm{V} \mathrm{rms}, 60-\mathrm{Hz}\) AC power.

Short Answer

Expert verified
After calculating in Step 1, you will get a certain value for \(X_C\). Then, you simply divide the voltage value (120 V) by \(X_C\) to find the rms current in amperes (A). Remember to consider the unit of measurement for your answer.

Step by step solution

01

Find the Capacitive Reactance \(X_C\)

First we need to calculate the capacitive reactance using the formula \(X_C = 1 / (2 \pi f C)\). Plug \(f = 60 Hz\) and \(C = 1.0 \mu F = 1.0 x 10^{-6} F\) into the formula to get the value of \(X_C\).
02

Find the RMS Current

Next, we use the formula for the rms current in an AC circuit, which is \(I = V / X_C\). With \(V = 120 V\), and the \(X_C\) value from Step 1, we can find the rms current \(I\).

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Most popular questions from this chapter

An AC voltage of fixed amplitude is applied across a series \(R L C\) circuit. The components are such that the current at half the resonant frequency is half the current at resonance. Show that the current at twice the resonant frequency is also half the current at resonance.

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

A car-battery charger runs off the \(120-\mathrm{V}\) rms AC power line and supplies \(10-\mathrm{A}\) DC at \(14 \mathrm{V}\). (a) If the charger is \(80 \%\) efficient in converting the line power to the DC power it supplies to the battery, how much current does it draw from the AC line? (b) If electricity costs \(9.5 \notin / \mathrm{kWh}\), how much does it cost to run the charger for 10 hours if the power factor is \(1 ?\)

An RLC circuit includes a 1.5 -H inductor and a \(250-\mu \mathrm{F}\) capacitor rated at 400 V. The circuit is connected across a sine-wave generator with \(V_{\mathrm{p}}=32 \mathrm{V} .\) What minimum resistance will ensure that the capacitor voltage does not exceed its rated value when the circuit is at resonance?

The same AC voltage appears across a capacitor and a resistor, and the same rms current flows in each. Is the power dissipation the same in each?
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