/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 A portable heater is connected t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 21: Problem 66

A portable heater is connected to a \(60-\mathrm{Hz}\) ac outlet. How many times per second is the instantancous power a maximum?

Short Answer

Expert verified
Answer: The instantaneous power in an AC circuit reaches its maximum value 120 times per second at a frequency of 60 Hz.

Step by step solution

01

Understand the relationship between power and frequency in an AC circuit

In an AC circuit, the instantaneous power is given by the formula \(P(t) = VI\cos(\phi)\cos(2\pi ft)\). Here, \(V\) is the instantaneous voltage, \(I\) is the instantaneous current, \(\phi\) is the phase angle between voltage and current, and \(f\) is the frequency. \(P(t)\) is a maximum when \(\cos(2\pi ft) = \pm 1\).
02

Calculate the number of times the power hits a maximum in a single cycle

Within one AC cycle, which occurs each \(\frac{1}{f}\) seconds, \(\cos(2\pi ft)\) will equal \(\pm 1\) twice. Since there are \(2\pi\) radians in a full cycle and \(\cos(x) = \pm 1\) where \(x=2n\pi\) (where n is an integer), we can deduce that the power would maximize twice at \(2n\pi = 2\pi\) and \(2n\pi = 4\pi\) within that cycle.
03

Multiply the number of maximum power instances in a single cycle by the frequency to find the final answer

As established in step 2, the power maximizes twice in a single cycle. Therefore, for a frequency of \(60 Hz\), the power will hit its maximum value \(60 * 2 = 120\) times per second.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) What mas current is drawn by a \(4200-\mathrm{W}\) electric room heater when running on \(120 \mathrm{V}\) rms? (b) What is the power dissipation by the heater if the voltage drops to \(105 \mathrm{V}\) rms during a brownout? Assume the resistance stays the same.
(a) What is the reactance of a 5.00 - \(\mu \mathrm{F}\) capacitor at the frequencies \(f=12.0 \mathrm{Hz}\) and \(1.50 \mathrm{kHz} ?\) (b) What is the impedance of a series combination of the \(5.00-\mu \mathrm{F}\) capacitor and a \(2.00-\mathrm{k} \Omega\) resistor at the same two frequencies? (c) What is the maximum current through the circuit of part (b) when the ac source has a peak voltage of \(2.00 \mathrm{V} ?\) (d) For each of the two frequencies, does the current lead or lag the voltage? By what angle?
An RLC series circuit is driven by a sinusoidal emf at the circuit's resonant frequency. (a) What is the phase difference between the voltages across the capacitor and inductor? [Hint: since they are in series, the same current \(i(t) \text { flows through them. }]\) (b) At resonance, the rms current in the circuit is \(120 \mathrm{mA}\). The resistance in the circuit is \(20 \Omega .\) What is the rms value of the applied emf? (c) If the frequency of the emf is changed without changing its rms value, what happens to the rms current? (W) tutorial: resonance)
A variable inductor with negligible resistance is connected to an ac voltage source. How does the current in the inductor change if the inductance is increased by a factor of 3.0 and the driving frequency is increased by a factor of \(2.0 ?\)
Finola has a circuit with a \(4.00-\mathrm{k} \Omega\) resistor, a \(0.750-\mathrm{H}\) inductor, and a capacitor of unknown value connected in series to a \(440.0-\mathrm{Hz}\) ac source. With an oscilloscope, she measures the phase angle to be \(25.0^{\circ} .\) (a) What is the value of the unknown capacitor? (b) Finola has several capacitors on hand and would like to use one to tune the circuit to maximum power. Should she connect a second capacitor in parallel across the first capacitor or in series in the circuit? Explain. (c) What value capacitor does she need for maximum power?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Physics of Motion

Read Explanation

Oscillations

Read Explanation

Particle Model of Matter

Read Explanation

Physical Quantities And Units

Read Explanation

Electromagnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.