Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 36

A transformer with a primary coil of 1000 turns is used to step up the standard \(170-\mathrm{V}\) amplitude line voltage to a \(220-\mathrm{V}\) amplitude. How many turns are required in the secondary coil?

Short Answer

Expert verified
Answer: 1295 turns.

Step by step solution

01

Recall the transformer turns ratio formula

The transformer turns ratio formula is given by: $$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$ Where \(V_p\) is the primary voltage, \(V_s\) is the secondary voltage, \(N_p\) is the primary coil turns, and \(N_s\) is the secondary coil turns.
02

Plug in the given values

We are given the primary coil turns \(N_p = 1000\), the primary voltage \(V_p = 170\,\mathrm{V}\), and the secondary voltage \(V_s = 220\,\mathrm{V}\). Our task is to find the secondary coil turns \(N_s\). We can plug the values into the formula: $$\frac{170}{220} = \frac{1000}{N_s}$$
03

Solve for the secondary coil turns

To find \(N_s\), we can cross-multiply and then solve for \(N_s\): $$170 \times N_s = 1000 \times 220$$ $$N_s = \frac{1000 \times 220}{170}$$ $$N_s = 1294.1176$$ Since the number of turns in a coil must be an integer, we round up to the nearest whole number: $$N_s = 1295$$ So, there are 1295 turns required in the secondary coil to step up the voltage from 170V to 220V.

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

An ideal inductor of inductance \(L\) is connected to an ac power supply, which provides an emf \(\mathscr{E}(t)=\mathscr{E}_{\mathrm{m}}\) sin \(\omega t\) (a) Write an expression for the current in the inductor as a function of time. [Hint: See Eq. \((20-7) .]\) (b) What is the ratio of the maximum emf to the maximum current? This ratio is called the reactance. (c) Do the maximum emf and maximum current occur at the same time? If not, how much time separates them?
A 2 -m-long copper pipe is held vertically. When a marble is dropped down the pipe, it falls through in about 0.7 s. A magnet of similar size and shape takes much longer to fall through the pipe. (a) As the magnet is falling through the pipe with its north pole below its south pole, what direction do currents flow around the pipe above the magnet? Below the magnet (CW or CCW as viewed from the top)? (b) Sketch a graph of the speed of the magnet as a function of time. [Hint: What would the graph look like for a marble falling through honey?]
When the armature of an ac generator rotates at $15.0 \mathrm{rad} / \mathrm{s},\( the amplitude of the induced emf is \)27.0 \mathrm{V}$ What is the amplitude of the induced emf when the armature rotates at $10.0 \mathrm{rad} / \mathrm{s} ?$ (tutorial: generator)
How much energy due to Earth's magnetic field is present in $1.0 \mathrm{m}^{3}$ of space near Earth's surface, at a place where the field has magnitude \(0.45 \mathrm{mT} ?\)
(a) For a particle moving in simple harmonic motion, the position can be written \(x(t)=x_{\mathrm{m}}\) cos \(\omega t .\) What is the velocity \(v_{x}(t)\) as a function of time for this particle? (b) Using the small-angle approximation for the sine function, find the slope of the graph of \(\Phi(t)=\Phi_{0} \sin \omega t\) at \(t=0 .\) Does your result agree with the value of \(\Delta \Phi / \Delta t=\omega \Phi_{0} \cos \omega t\) at \(t=0 ?\)
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Energy Physics

Read Explanation

Rotational Dynamics

Read Explanation

Fluids

Read Explanation

Dynamics

Read Explanation

Thermodynamics

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