Conceptual Physics

Variables

Strategy

1. State Faraday’s law twice, for the emf induced across each coil by the changing
   magnetic flux. The emf equals the potential difference across the components.


2. Divide the two equations.

Physics principles and equations

Faraday’s law stated in terms of potential difference, and for a coil of N loops, is

With transformers, it is traditional to refer to potential differences rather than emfs in the

primary and secondary windings.

Step-by-step derivation

We state Faraday’s law for each coil, then divide the two equations and simplify the

result.

Transformers can increase a potential difference, but by now you have learned that in

physics, you do not get something without also giving something up. The principle of

conservation of energy must apply to transformers. How does this precept apply? It

requires that the power, or energy produced or consumed per unit time, is the same on

both sides of an ideal transformer. Power equals the current times the potential

difference. If you boost the potential difference, you decrease the current.

The ratio of the currents is the inverse of the turns ratio. This is shown in Equation 2.

The example problem asks you to analyze a type of transformer commonly sold in

travel stores. This transformer steps down European voltage (240 V AC) to USA

standard voltage (120 V AC), and you may need one if you intend to use any of your

personal appliances on a trip abroad.

Potential differences ratio equals

turns ratio

ǻV 1 = primary potential difference

ǻV 2 = secondary potential difference

N 1 = primary number of loops

N 2 = secondary number of loops

Currents ratio is inverse of turns

ratio

I 1 = primary current

I 2 = secondary current

What should the turns ratio of

the transformer be?

potential difference across primary coil ǻV 1

potential difference across secondary coil ǻV 2

number of loops in primary coil N 1

number of loops in secondary coil N 2

time interval ǻt

change in magnetic flux through one loop during ǻt ǻĭB

Step Reason

1. Faraday’s law

2. Faraday’s law

3. divide

4. simplify

(^550) Copyright 2007 Kinetic Books Co. Chapter 29