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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

A hair dryer has a power rating of \(1200 \mathrm{W}\) at \(120 \mathrm{V}\) rms. Assume the hair dryer circuit contains only resistance. (a) What is the resistance of the heating element? (b) What is the rms current drawn by the hair dryer? (c) What is the maximum instantaneous power that the resistance must withstand?
Transformers are often rated in terms of kilovolt-amps. A pole on a residential street has a transformer rated at $35 \mathrm{kV} \cdot \mathrm{A}$ to serve four homes on the strect. (a) If each home has a fuse that limits the incoming current to \(60 \mathrm{A}\) rms at \(220 \mathrm{V}\) rms, find the maximum load in \(\mathrm{kV} \cdot \mathrm{A}\) on the transformer. (b) Is the rating of the transformer adequate? (c) Explain why the transformer rating is given in kV.A rather than in kW.
A \(1500-\) W heater runs on \(120 \mathrm{V}\) ms. What is the peak current through the heater? (Wtorial: power in ac circuits)
A solenoid with a radius of \(8.0 \times 10^{-3} \mathrm{m}\) and 200 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of \(15 \mathrm{V}\) ms at \(22 \mathrm{kHz}\), an \(\mathrm{rms}\) current of \(3.5 \times 10^{-2} \mathrm{A}\) is measured. Assume the resistance of the solenoid is negligible. (a) What is the inductive reactance? (b) What is the length of the solenoid?
An x-ray machine uses \(240 \mathrm{kV}\) rms at \(60.0 \mathrm{mA}\) ms when it is operating. If the power source is a \(420-\mathrm{V}\) rms line, (a) what must be the turns ratio of the transformer? (b) What is the rms current in the primary? (c) What is the average power used by the \(x\) -ray tube?
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