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Chapter 28: Problem 15

An industrial electric motor runs at \(208 \mathrm{V}\) rms and \(400 \mathrm{Hz}\). What are (a) the peak voltage and (b) the angular frequency?

Short Answer

Expert verified
The peak voltage and the angular frequency of the industrial electric motor are approximately 294.28 V and \(2513.27 rad/s\) respectively.

Step by step solution

01

Calculating Peak Voltage

Given the RMS voltage is 208 V, peak voltage can be calculated using the formula \( V_{peak} = \sqrt{2} * V_{rms} \). Substituting the given value into the formula gives \( V_{peak} = \sqrt{2} * 208 \approx 294.28 V \)
02

Calculating Angular Frequency

Given the frequency is 400 Hz, the angular frequency can be calculated using the formula \( \omega = 2\pi f \). Substituting the given value into the formula gives \( \omega = 2\pi* 400 \approx 2513.27 rad/s \)

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Most popular questions from this chapter

For \(R L C\) circuits in which the resistance isn't too high, the \(Q\) factor may be defined as the ratio of the resonant frequency to the difference between the two frequencies where the power dissipated in the circuit is half the power dissipated at resonance. Using suitable approximations, show that this definition leads to \(Q=\omega_{0} L / R,\) with \(\omega_{0}\) the resonant frequency.

Why does it make sense that inductive reactance increases with frequency?

An AC current is given by \(I=495 \sin (9.43 t),\) with \(I\) in \(\mathrm{mA}\) and \(t\) in ms. Find (a) the rms current and (b) the frequency in Hz.

A 2.0 - \(\mu\) F capacitor has 1.0 -k \(\Omega\) reactance. (a) What's the frequency of the applied voltage? (b) What inductance would give the same reactance at this frequency? (c) How would the reactances compare if the frequency were doubled?

An RLC circuit includes a \(1.5-\mathrm{H}\) inductor and a \(250-\mu \mathrm{F}\) capacitor rated at 400 V. The circuit is connected across a sine-wave generator with \(V_{\mathrm{p}}=32 \mathrm{V} .\) What minimum resistance will ensure that the capacitor voltage does not exceed its rated value when the circuit is at resonance?
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