Transformer examples

Now we know

$V_1/V_2=(Number\ \turns\ \1)/(Number\ \turns\ \2)$

and

$V_1xxI_1=V_2xxI_2$

We can now work out many problems.

Example 1

A transformer converts 40 volts of alternating current to a higher voltage. The current in the primary coil is 12 amps and the secondary side is 4 amps.

Question A – What is the secondary voltage?

So if we write out all the formulae:

$V_1/V_2=(Number\ \turns\ \1)/(Number\ \turns\ \2)$ .......1

$V_1xxI_1=V_2xxI_2$ ........2

using formula 2 we have:

$40xx12=V_2xx4$

therefore

$V_2=(40xx12)/4=120\ \v\o\l\t\s$

There are 120 volts produced in the secondary side.

Question B – If there are 100 primary coils, how many secondary coils are there?

Using formula 1 we have:

$40/120=100/(Numer\ \turns\ \2)$

$Turns\ \2=(100xx120)/40$

$Turns\ \2=100xx3$

$Turns\ \2=300$

There are 300 turns on the secondary side.

Example 2

A transformer is 100% efficient. It has 200 turns on the primary coil and an input current of 0.5amps. If the secondary coil has 3,000 turns what is the output current?

We know

$V_1/V_2=N_1/N_2$

and also

$V_1\ \I_1=V_2\ \I_2$

Therfore

$V_1/V_2=I_2/I_1$

and therefore

$I_2/I_1=N_1/N_2$

Using this last formula we get

$I_2/0.5amps=(200\ \turns)/(3000\ \turns)$

$I_2=(200xx0.5)/3000$

$I_2=0.033dot3\ \amps$

The output current is $0.033dot3\ \amps$

Example 3

An AC power supply is connected to a transformer. The AC power supply is 12 volts and 2.5 amps. The secondary coil gives a reading of 4 volts.

i. Calculate the power input to the transformer.

We know Power = Village Idiot (see mnemonic)

$P=VI$

Therefore

$P=12xx2.5=30\ \w\a\t\t\s$

ii. Calculate the current in the secondary coil.

We know power cannot be lost or gained

Voltage $1xx$ Current $1$ = Primary power = Secondary power = Voltage $2xx$ Current $2$

$V_1\ \I_1=V_2\ \I_2$

$12xx2.5=4xxI_2$

$I_2=(12xx2.5)/4$

$I_2=7.5\ \amps$

iii. The primary coil has 15 turns; how many turns does the secondary coil have?

We know

$V_1/V_2=N_1/N_2$

$12/4=15/N_2$

$N_2=(15xx4)/12$

$N_2=5\ \turns$