# The percentage resistance and percentage reactance of a 10 kVA, 400 V/200 V, 3- phase transformer are 2% and 10% respectively.

The percentage resistance and percentage reactance of a 10 kVA, 400 V/200 V, 3- phase transformer are 2% and 10% respectively. If the constant losses in the machine are 1%, the maximum possible percentage efficiency of the transformer is

#### SOLUTION

Since Full Load Copper loss = R P.U

= 0.02 P.U

Iron Loss = Pi = 0.01 P.u

In case of Max efficiency of transformer the copper loss and Iron loss are equal i.e Pi = Pc

If x is the fraction of full load than transformer efficiency is given as

$\begin{array}{l}{\eta _{Max}} = \dfrac{{x \times output}}{{x \times output + 2{P_i}}}\\\\x = \sqrt {\dfrac{{{\text{Iron Loss}}}}{{{\text{FL Copper Loss}}}}} \\\\x = \sqrt {\dfrac{1}{2}} = 0.707\\\\{\eta _{Max}} = \dfrac{{0.707 \times 1}}{{0.707 \times 1 + 2 \times 0.01}}\end{array}$

ηmax = 97.25 %

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