This test is conducted instantaneously on two similar transformers and so the transformers temperature rise, efficiency and voltage regulations. The advantage of conducting this test is very economical of power, even when the transformers are tested at full load conditions. The total losses of both the transformers are equal to the power required to conduct this test. It might be noted to carry out this test that the two transformer needs to be identical.

### Circuit Diagram

The figure above shows that the connection diagram of back to back test on two similar transformers named T

_{1}and T_{2}. The two transformers primary windings are parallel connected across the rated supply voltage V_{1}and the secondary windings of the transformers are connected opposition in phase. Hence the circulating current formed in the loop of secondary’s will be zero because EMF induced in the transformers are equal and in opposition. There is an auxiliary low voltage in the transformer which can be varied to provide an adjustable voltage and so current in secondary circuit loop. The volt-meter V_{1}, amp-meter A_{1}and watt-meter W_{1}are connected in the primary side (input) of the transformer. An amp-meter A_{2}and watt-meter W_{2}are connected in secondary (output side) of the transformer.### Working:

The transformer secondary sides are in phase opposition. Then switch S

_{2}is open and switch S_{1}is closed, thus the circulating current in the transformer secondary circuit loop is zero (i.e. I_{2}=0). This is due to EMF induced in the secondary’s are in equal and opposition. This circumstance is just like an open circuit test. Hence the current drawn from the source is 2I_{0}. The wattmeter reading W_{1}and the core loss of both the transformers are equal.
I

_{0}= No load current of every transformer
W

_{1}= Core losses of both the transformers.
Now switch S

_{2}also closed and the voltage at the output of the regulating transformer is varied until the full load current I_{2}drift in the secondary circuit loop. The secondary full load current will cause full load current I_{1}in the primary circuit. The full load current I_{1}will circulates in the primary winding alone. The two transformers full load copper losses is equal wattmeter W_{2}reading since the full load current circulating through the primary winding and secondary windings.
W

_{2}= Transformer full load copper losses
W

_{2}+W_{1}= Total losses of the two transformers at full load.#### During this test the following point may be noted:

- The wattmeter’s W
_{1}& W_{2}gives the core losses and copper losses at full load of the two transformers respectively. Hence the total losses of two transformers are equal to the power required to conduct this test. - The total iron losses and copper losses at full load are occurring even though the transformers are not supplying any load.
- There are two voltage supply; one is transformer regulating voltage and the other is supply voltage and in between these voltages no interference. The source voltage provides 2I
_{0}while the transformer regulating voltage provides I2 and thus I_{1}=KI_{2}.

#### Advantages of this test:

- Little much of power is required to conduct this test
- Under full load conditions transformers can be test using this test.
- Simultaneously full load copper losses and iron losses are measured
- The secondary current I
_{2}can be varied at any value of the current. Hence we can determine the copper losses at full load condition or at any load. - The transformer temperature increase can be noted.