# 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`