Answered: A transformer is designed for use in a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A transformer is designed for use in a model train. The input voltage is 120 V and the output needs to be 9.0V. The output current will be 2.50A.

If 1000 turns are placed on the primary coil, how many turns will need to be on the secondary coil?

1. What is the current in the primary set of coils?

2. What is the power output of the transformer?

Expert Solution

Step 1

Given:

The input voltage is $120 V$ .

The output voltage is $9.0 V$ .

The output current is $2.50 A$ .

Introduction:

A transformer is used to step up or step down the output voltage. The output voltage depends upon the number of turns in the primary and secondary coils of the transformer.

Step 2

Calculation:

(1)

Write the expression for the transformer ratio.

$\frac{V_{p}}{V_{s}} = \frac{I_{s}}{I_{p}}$

Here, $V_{p}$ is the input voltage in the primary coil, $V_{s}$ is the output voltage in the secondary coil, $I_{s}$ is the output current and $I_{p}$ is the input current.

Substitute, $120 V$ for $V_{p}$ , $9.0 V$ for $V_{s}$ and $2.50 A$ for $I_{s}$ in the above expression.

$\begin{array}{rcl} \frac{120 V}{9.0 V} & = & \frac{2.50 A}{I_{p}} \\ I_{p} & = & \frac{2.50 A (9.0 V)}{(120 V)} \\ I_{p} & = & 0.187 A \end{array}$

Thus, the input current in the primary coil is $0.187 A$ .

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