CK-12-Physics - Intermediate

19.3. Electrical Power Transfer http://www.ck12.org

FIGURE 19.10

Vs= 2 Vp

Thus, this transformer is a step-up transformer.

IfNs<Np, we have a step-down transformer, in which the secondary voltage is less than the primary voltage.

It may seem like we’re getting more out of the step-up transformer than we’re putting into it and less out of the

step-down transformer than we put into it. This is not the case, however. Keep in mind that only energy is expected

to be conserved, not voltage. Energy conservation implies that, if no energy is transformed into heat, then the output

power of the primary coil must be equal to the input power of the secondary coil.

Recalling thatP=IV:

IpVp=IsVs(Transformer Equation B)

We see that in a step-up transformer, if the voltage increases by a factor ofn, then the current must decrease by the

same factor ofn. Similarly, in a step-down transformer, if the voltage decreases by a factorm, then the current must

increase by the same factor ofm. (All that is true assuming no energy loss due to Joule heat, which is, of course,

impossible in real life.)

Using Equations A and B, we see:

Vp

Vs

=

Is

Ip

→

Ip

Is

=

Ns

Np

(Transformer Equation C)

Thus, the ratio of the currents is equal to the inverse ratio of the number of turns in the corresponding coils.

Check Your Understanding

a. A generating station step-up transformer has an input voltage of 12,000 V with 100 turns on the primary coil. If

the secondary coil is to have an output voltage of 300,000 V, how many turns must the secondary coil have? Assume

no energy is transferred to heat.

Answer: