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Chapter 28: Problem 5

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?

Short Answer

Expert verified
No, the power dissipation is not the same in each. Power is dissipated in the resistor but not in the capacitor.

Step by step solution

01

Analyze Power Dissipation in Resistor

In a resistor, the voltage and current are in phase in an AC circuit. Therefore, power (P) can be computed using Ohm's Law, \(P = I^2R\), where I is the current and R is the resistance.
02

Analyze Power Dissipation in Capacitor

In a capacitor, the voltage and current are 90° out of phase in an AC circuit. Thus, the power dissipated across the capacitor is zero because the power (P) in an AC circuit is also given as \(P = VIcos(φ)\), where V is the voltage, I is the current, and φ is the phase difference between the current and voltage. Since for a capacitor φ=90°, \(cos(90°) = 0\), thereby making \(P = 0\).
03

Compare power dissipation

Compare the power dissipation in the resistor and the capacitor. It is evident that the power dissipation in the resistor is \(I^2R\) and power dissipation in the capacitor is 0. Hence, the power dissipation is not the same in each

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