**Sumpner's test or back to back test on transformer**is another method for determining transformer efficiency, voltage regulation and heating under loaded conditions. Short circuit and open circuit tests on transformer can give us parameters of equivalent circuit of transformer, but they can not help us in finding the heating information. Unlike O.C. and S.C. tests, actual loading is simulated in Sumpner's test. Thus the Sumpner's test give more accurate results of regulation and efficiency than O.C. and S.C. tests.

## Sumpner's test

Sumpner's test or back to back test can be employed only when two identical transformers are available. Both transformers are connected to supply such that one transformer is loaded on another. Primaries of the two identical transformers are connected in parallel across a supply. Secondaries are connected in series such that emf's of them are opposite to each other. Another low voltage supply is connected in series with secondaries to get the readings, as shown in the circuit diagram shown below.

In above diagram, T

i.e. iron loss per transformer Pi = W

Now, a small voltage V

i.e. copper loss per transformer P

From above test results, the

In above diagram, T

_{1}and T_{2}are identical transformers. Secondaries of them are connected in voltage opposition, i.e. E_{EF}and E_{GH}. Both the emf's cancel each other, as transformers are identical. In this case, as per superposition theorem, no current flows through secondary. And thus the no load test is simulated. The current drawn from V_{1}is 2I_{0}, where I_{0}is equal to no load current of each transformer. Thus input power measured by wattmeter W_{1}is equal to iron losses of both transformers.i.e. iron loss per transformer Pi = W

_{1}/2.Now, a small voltage V

_{2}is injected into secondary with the help of a low voltage transformer. The voltage V_{2}is adjusted so that, the rated current I_{2}flows through the secondary. In this case, both primaries and secondaries carry rated current. Thus short circuit test is simulated and wattmeter W_{2}shows total full load copper losses of both transformers.i.e. copper loss per transformer P

_{Cu}= W_{2}/2.From above test results, the

**full load efficiency of each transformer**can be given as -