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Chapter 21: Problem 40

A computer draws an rms current of \(2.80 \mathrm{A}\) at an \(\mathrm{rms}\) voltage of \(120 \mathrm{V}\). The average power consumption is 240 W. (a) What is the power factor? (b) What is the phase difference between the voltage and current?

Short Answer

Expert verified
PF = 0.7143 (approximately) #tag_title#Step 3: Calculate the Phase Difference#tag_content#Now we can find the phase difference (θ) using the formula: θ = arccos(PF) Plug in the power factor value we found earlier:#tag_code# import math math.acos(0.7143)

Step by step solution

01

Information from the exercise

We are given: - rms current \((I) = 2.80 A\) - rms voltage \((V) = 120 V\) - average power \((P_{avg}) = 240 W\)
02

Calculate the Power Factor

The power factor (PF) is defined as the ratio of average power to the product of rms current and rms voltage. So, PF = \(\dfrac{P_{avg}}{IV}\) Plugging in the given values: PF = \(\dfrac{240}{2.80 \times 120}\) Now, calculate the power factor value:#tag_code# 240/(2.80*120)

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Make a figure analogous to Fig. 21.4 for an ideal inductor in an ac circuit. Start by assuming that the voltage across an ideal inductor is \(v_{\mathrm{L}}(t)=V_{\mathrm{L}}\) sin \(\omega t .\) Make a graph showing one cycle of \(v_{\mathrm{L}}(t)\) and \(i(t)\) on the same axes. Then, at each of the times \(t=0, \frac{1}{8} T, \frac{2}{8} T, \ldots, T,\) indicate the direction of the current (or that it is zero), whether the current is increasing, decreasing, or (instantaneously) not changing, and the direction of the induced emf in the inductor (or that it is zero).
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