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Chapter 21: Problem 76

What is the rins current flowing in a \(4.50-\mathrm{kW}\) motor connected to a \(220-\mathrm{V}\) rms line when (a) the power factor is 1.00 and (b) when it is \(0.80 ?\)

Short Answer

Expert verified
Answer: The rms currents flowing in the motor are approximately 20.45 A at a power factor of 1.00 and approximately 25.57 A at a power factor of 0.80.

Step by step solution

01

Write down the given information and the formula for power

We are given the following information: - Power of the motor: P = 4.50 kW - Voltage of the power source: V = 220 V - Two power factors: (a) pf = 1.00, (b) pf = 0.80 We will use the formula for power: \(P = V \times I \times pf\)
02

Convert the power to watts

Since the given power is in kW, we need to convert it to watts: Power in watts, P = 4.50 kW * 1000 = 4500 W
03

Calculate the rms current for power factor 1.00

Using the formula for power, we can rearrange to solve for the current I: \( I = \frac{P}{V \times pf} \) For the power factor pf = 1.00, calculate I: \( I = \frac{4500}{220 \times 1.00} \approx 20.45 A\)
04

Calculate the rms current for power factor 0.80

For the power factor pf = 0.80, calculate I: \( I = \frac{4500}{220 \times 0.80} \approx 25.57 A\)
05

Summarize the results

So, the rms current flowing in the 4.50-kW motor connected to a 220-V rms line: (a) when the power factor is 1.00, the rms current is approximately 20.45 A (b) when the power factor is 0.80, the rms current is approximately 25.57 A

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Most popular questions from this chapter

An RLC series circuit is connected to a \(240-\mathrm{V}\) ms power supply at a frequency of \(2.50 \mathrm{kHz}\). The elements in the circuit have the following values: \(R=12.0 \Omega, C=\) \(0.26 \mu \mathrm{F},\) and $L=15.2 \mathrm{mH},$ (a) What is the impedance of the circuit? (b) What is the rms current? (c) What is the phase angle? (d) Does the current lead or lag the voltage? (e) What are the rms voltages across each circuit element?
A capacitor is rated at \(0.025 \mu \mathrm{F}\). How much rms current flows when the capacitor is connected to a \(110-\mathrm{V}\) rms, \(60.0-\mathrm{Hz}\) line?
A series \(R L C\) circuit has a \(0.20-\mathrm{mF}\) capacitor, a \(13-\mathrm{mH}\) inductor, and a \(10.0-\Omega\) resistor, and is connected to an ac source with amplitude \(9.0 \mathrm{V}\) and frequency \(60 \mathrm{Hz}\) (a) Calculate the voltage amplitudes \(V_{L}, V_{C}, V_{R},\) and the phase angle. (b) Draw the phasor diagram for the voltages of this circuit.
An \(R L C\) series circuit has a resistance of \(R=325 \Omega\) an inductance \(\quad L=0.300 \mathrm{mH}, \quad\) and \(\quad\) a capacitance $C=33.0 \mathrm{nF} .$ (a) What is the resonant frequency? (b) If the capacitor breaks down for peak voltages in excess of \(7.0 \times 10^{2} \mathrm{V},\) what is the maximum source voltage amplitude when the circuit is operated at the resonant frequency?
A \(150-\Omega\) resistor is in series with a \(0.75-\mathrm{H}\) inductor in an ac circuit. The rms voltages across the two are the same. (a) What is the frequency? (b) Would each of the rms voltages be half of the rms voltage of the source? If not, what fraction of the source voltage are they? (In other words, \(V_{R} / \ell_{m}=V_{L} / \mathcal{E}_{m}=?\) ) (c) What is the phase angle between the source voltage and the current? Which leads? (d) What is the impedance of the circuit?
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