Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 28: Problem 44

A \(0.75-\mathrm{H}\) inductor is in series with a fluorescent lamp, and the combination is across \(120-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) power. If the rms inductor voltage is \(90 \mathrm{V},\) what's the rms lamp current?

Short Answer

Expert verified
The rms lamp current is 0.318 A.

Step by step solution

01

Calculate the Total RMS Voltage

In this case, the total rms voltage across the lamp and inductor is given as 120V. This refers to the phasor sum of the rms voltage across the lamp and that across the inductor. Using the Pythagorean theorem, \(V_{lamp} = \sqrt{V_{total}^2 - V_{inductor}^2} = \sqrt{120^2 - 90^2} = 72 V\).
02

Use Ohm’s Law

The RMS current can be obtained by using Ohm's Law, which states that \(V = I \cdot Z\), where V is the voltage, I is the current and Z is the impedance. Here impedance \(Z_{inductor} = 2 \cdot \pi \cdot f \cdot L\), where \(f = 60\) Hz is the frequency, \(L = 0.75 H\) is the inductance. So, \(Z_{inductor} = 2 \cdot \pi \cdot 60 \cdot 0.75 = 282.74 \) Ohm.
03

Calculate the current

Substitute the inductor impedance and RMS voltage into Ohm's law to solve for the current: \(I = \frac{V_{inductor}}{Z_{inductor}} = \frac{90V}{282.74 \, \Omega} = 0.318 \, A\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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 series \(R L C\) circuit with \(R=1.3 \Omega, L=27 \mathrm{mH},\) and \(C=\) \(0.33 \mu \mathrm{F}\) is connected across a sine-wave generator. If the capacitor's peak voltage rating is \(600 \mathrm{V},\) what's the maximum safe value for the generator's peak output voltage when it's tuned to resonance?

Much of Europe uses AC power at \(230 \mathrm{V}\) rms and \(50 \mathrm{Hz}\). Express this AC voltage in the form of Equation \(28.3,\) taking \(\phi_{V}=0\)

A \(470-\Omega\) resistor, \(10-\mu \mathrm{F}\) capacitor, and \(750-\mathrm{mH}\) inductor are each connected across \(6.3-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) AC power. Find the rms current in each.

You're Chief Financial Officer for a power company, and you consult your engineering department in an effort to minimize power-line losses. Your power plant produces \(60-\mathrm{Hz}\) power at \(365 \mathrm{kV} \mathrm{rms}\) and \(200 \mathrm{A} \mathrm{rms},\) and delivers it via transmission lines with total resistance \(100 \Omega .\) You ask the engineers for the percentage of power that's lost. They reply that it depends on the power factor. What's the percentage loss for power factors of (a) 1.0 and (b) \(0.60 ?\)

Your university's FM station broadcasts at \(89.5 \mathrm{MHz}\). The \(L C\) circuit that establishes this frequency has a 47 -pF capacitor. What's the corresponding inductance?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Physical Quantities And Units

Read Explanation

Mechanics and Materials

Read Explanation

Scientific Method Physics

Read Explanation

Physics of Motion

Read Explanation

Quantum Physics

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.

Sign-up for free