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Chapter 28: Problem 35

An electric water heater draws \(20 \mathrm{A}\) rms at \(240 \mathrm{V}\) rms and is purely resistive. An AC motor has the same current and voltage, but inductance causes the voltage to lead the current by \(20^{\circ} .\) Find the power consumption in each device.

Short Answer

Expert verified
After evaluation, the power consumption of the water heater should be found to be \(4800\) Watts, which is the same as the apparent power because of no phase difference. However, the power consumption of the AC motor, due to the phase difference, will be less than the heater and should be approximately \(4518.04\) Watts.

Step by step solution

01

Calculate Power for Water Heater

Since the heater is pure resistive, the power factor is \(1\), and the phase angle \(\phi\) is \(0^{\circ}\). Therefore, the power consumption \(P_r\) of the heater can be calculated using the formula - \(P = VI \cos \phi\), where \(V\) is the voltage and \(I\) is the current. Substituting the given values, we get: \(P = 240V \times 20A \times \cos (0)\)
02

Calculate Power for AC Motor

For the AC motor, the phase angle \(\phi\) is \(20^{\circ}\), due to the inductance. Thus, the power consumption \(P_l\) can be calculated using the same formula but the cosine of the phase angle must be considered. Substituting the given values, we get: \(P = 240V \times 20A \times \cos (20)\)
03

Evaluate the Expressions

In step 1 and step 2, evaluate the power expressions for both devices. Ensure that the cosine function is working in degrees, not radians.

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Most popular questions from this chapter

You're asked to experiment with a series \(R L C\) circuit consisting of a \(10-\Omega\) resistor, \(50-\mathrm{mH}\) inductor, and \(1.5-\mu \mathrm{F}\) capacitor rated at \(1200 \mathrm{V} .\) You're to apply a sinusoidal AC voltage peaking at \(100 \mathrm{V} .\) But you're worried there might be a chance you'll exceed the capacitor's rated voltage. Your lab partner claims this can't happen, since the capacitor rating is 12 times the peak voltage of the AC source. Who's right? To find out, plot the peak capacitor voltage as a function of frequency. Is there a frequency range you should avoid?

A series \(R L C\) circuit has \(R=18 \mathrm{k} \Omega, L=20 \mathrm{mH},\) and resonates at \(4.0 \mathrm{kHz}\). (a) What's the capacitance? (b) Find the circuit's impedance at resonance and (c) at \(3.0 \mathrm{kHz}\)

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?

An LC circuit with \(C=18\) mF undergoes oscillations with period \(2.4 \mathrm{s}\). Find the inductance.

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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