Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 2091

\(\mathrm{A}\) coil of inductance \(\mathrm{L}\) has an inductive reactance of \(\mathrm{X}_{\mathrm{L}}\) in an AC circuit in which the effective current is \(\mathrm{I}\). The coil is made from a super-conducting material and has no resistance. The rate at which power is dissipated in the coil is. (a) 0 (b) \(\mathrm{IX}_{\mathrm{L}}\) (c) \(I^{2} \mathrm{X}_{\mathrm{L}}\) (d) \(\mathrm{IX}^{2} \mathrm{~L}\)

Short Answer

Expert verified
The rate at which power is dissipated in the superconducting coil is 0.

Step by step solution

01

Understand the power formula in an AC circuit

In an AC circuit, the total power (P) can be represented as the product of the effective voltage (V) and the effective current (I) and the power factor (pf). The power factor represents the phase angle between the voltage and current in the circuit and can be calculated as: \[pf = \cos(\phi) \] where \(\phi\) is the phase angle between voltage and current. In this case, since the coil has no resistance, the phase angle will be 90 degrees, as the voltage and current are perpendicular to each other in an inductive circuit.
02

Calculate the power factor

Since the phase angle between voltage and current in an inductive circuit is 90 degrees: \[pf = cos(90 ^\circ) = 0\]
03

Calculate the power dissipation in the coil

Using the power formula with the calculated power factor, we can find the power dissipation in the coil: \[P = VI \cdot pf\] \[P = VI \cdot 0\] \[P = 0\]
04

Choose the correct answer

Based on our calculations, the rate at which power is dissipated in the coil is 0. Therefore, the correct answer is: (a) 0

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

Two co-axial solenoids are made by a pipe of cross sectional area $10 \mathrm{~cm}^{2}\( and length \)20 \mathrm{~cm}$ If one of the solenoid has 300 turns and the other 400 turns, their mutual inductance is...... (a) \(4.8 \pi \times 10^{-4} \mathrm{H}\) (b) \(4.8 \pi \times 10^{-5} \mathrm{H}\) (c) \(2.4 \pi \times 10^{-4} \mathrm{H}\) (d) \(4.8 \pi \times 10^{4} \mathrm{H}\)

A rectangular loop with a sliding rod of length \(2 \mathrm{~m} \&\) resistance \(2 \Omega\). It moves in a uniform magnetic field of \(3 \mathrm{~T}\) perpendicular to plane of loop. The external force required to keep the rod moving with constant velocity of \(2 \mathrm{~ms}^{-1}\) is

The resistance of a coil for dc is in ohms. In ac, the resistance (a) will remain same (b) will increase (c) will decrease (d) will be zero

An LC circuit contains a \(20 \mathrm{mH}\) inductor and a \(50 \mu \mathrm{F}\) capacitor with an initial charge of \(10 \mathrm{mc}\). The resistance of the circuit is negligible. At the instant the circuit is closed be \(t=0 .\) At what time is the energy stored completely magnetic. (a) \(\mathrm{t}=0 \mathrm{~ms}\) (b) \(\mathrm{t}=1.54 \mathrm{~ms}\) (c) \(\mathrm{t}=3.14 \mathrm{~ms}\) (d) \(\mathrm{t}=6.28 \mathrm{~ms}\)

A ring of radius \(\mathrm{r}\) is rotating about its diameter with angular velocity w in a perpendicular magnetic field \(\mathrm{B}^{-}\) It has 20 turns. The emf induced is (a) \(20 \mathrm{~B} \pi \mathrm{r}^{2} \sin \mathrm{wt}\) (b) \(20 \mathrm{~B} \pi \mathrm{r}^{2} \mathrm{cos} \mathrm{wt}\) (c) \(10 \sqrt{2} \mathrm{~B} \pi \mathrm{r}^{2}\) (d) \(20 \mathrm{~B} \pi \mathrm{r}^{2} \mathrm{w} \sin \mathrm{wt}\)
See all solutions

Recommended explanations on English Textbooks

Blog

Read Explanation

Summary Text

Read Explanation

Syntax

Read Explanation

Rhetoric

Read Explanation

Prosody

Read Explanation

Key Concepts in Language and Linguistics

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