Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 2079

The instantaneous value of current in an \(\mathrm{AC}\). circuit is \(\mathrm{I}=2 \sin [100 \pi \mathrm{t}+(\pi / 3)] \mathrm{A}\). The current will be maximum for the first time at, (a) \(\mathrm{t}=(1 / 100) \mathrm{sec}\) (b) \(\mathrm{t}=(1 / 200) \mathrm{sec}\) (c) \(t=(1 / 400) \mathrm{sec}\) (d) \(t=(1 / 600) \mathrm{sec}\)

Short Answer

Expert verified
The current will be maximum for the first time when \(t=\frac{1}{600}\) sec. So, the correct answer is (d) \(t=(1 / 600) sec\).

Step by step solution

01

Set up the equation for maximum current

We know that the current is maximum when the sine function is maximum. So, we will set up the equation as follows: \(100\pi t + (\pi/3) = \pi/2 + 2n\pi\)
02

Solve for t

To solve for t, we will isolate t in the equation as follows: \(100\pi t = \pi/2 + 2n\pi - \pi/3\) Now, divide both sides by \(100\pi\): \(t = \frac{\pi/2 + 2n\pi - \pi/3}{100\pi}\)
03

Find the smallest positive value of t

To get the smallest positive value of t, we can set n = 0 then solve for t: \(t = \frac{\pi/2 - \pi/3}{100\pi} = \frac{\pi/6}{100\pi} = \frac{1}{600} sec\) So, the current will be maximum for the first time at t = 1/600 sec, and the correct answer is (d) \(t=(1 / 600) sec\).

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 primary winding of transformer has 500 turns whereas its secondary has 5000 turns. Primary is connected to ac supply of \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) The secondary output of (a) \(200 \mathrm{~V}, 25 \mathrm{~Hz}\) (b) \(200 \mathrm{~V}, 50 \mathrm{~Hz}\) (c) \(2 \mathrm{~V}, 100 \mathrm{~Hz}\) (d) \(2 \mathrm{~V}, 50 \mathrm{~Hz}\)

The diagram shows a capacitor \(\mathrm{C}\) and resistor \(\mathrm{R}\) connected in series to an ac source. \(\mathrm{V}_{1}\) and \(\mathrm{V}_{2}\) are voltmeters and \(\mathrm{A}\) is an ammeter, consider the following statements.(a) Readings in \(\mathrm{A}\) and \(\mathrm{V}_{2}\) are always in phase. (b) Reading in \(\mathrm{V}_{1}\) is ahead in phase with reading in \(\mathrm{V}_{2}\). (c) Reading in \(\mathrm{A}\) and \(\mathrm{V}_{1}\) are always in phase. (d) Which of these statements are is correct (a) 1) only (b) 2) only (c) 1 ) and 2) only (d) 2 ) and 3) only

A conducting rod \(P Q\) of length \(4 \ell\) is rotated about a point \(O\) in a uniform magnetic field \(\mathrm{B} \rightarrow \mathrm{PO}=\ell\) Then (a) $\mathrm{V}_{\mathrm{Q}}-\mathrm{V}_{\mathrm{P}}=-\left[\left\\{\mathrm{B} \omega \ell^{2}\right\\} /\right.$ \(\\{2\\}] \quad\) (b) $\mathrm{V}_{\mathrm{Q}}-\mathrm{V}_{\mathrm{O}}=(5 / 2) \mathrm{B} \operatorname{co} \ell^{2}$ (c) $\mathrm{V}_{Q}-\mathrm{V}_{\mathrm{O}}=(9 / 2) \mathrm{B} \omega \ell^{2}$ (d) $\mathrm{V}_{\mathrm{P}}-\mathrm{V}_{\mathrm{Q}}=4 \mathrm{~B} \omega \ell^{2}$

\(220 \mathrm{~V}, 50 \mathrm{~Hz}\), ac is applied to a resistor. The instantaneous value of voltage is (a) \(220 \sqrt{2} \sin 100 \pi \mathrm{t}\) (b) \(220 \sin 100 \pi \mathrm{t}\) (c) \(220 \sqrt{2} \sin 50 \pi \mathrm{t}\) (d) \(220 \sin 50 \pi \mathrm{t}\)

In general in an alternating current circuit. (a) The average value of current is zero. (b) The average value of square of current is zero. (c) Average power dissipation is zero. (d) The phase difference between voltage and current is zero.
See all solutions

Recommended explanations on English Textbooks

Cues and Conventions

Read Explanation

Creative Story

Read Explanation

Syntax

Read Explanation

Sociolinguistics

Read Explanation

Synthesis Essay

Read Explanation

Linguistic Terms

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