Problem Set 1

Problem

Find the core inductance and resitence of a transformer using measurmnets Voc=5V, Ioc=3A, and Poc =10W.

Solution \! Power is found only through resister

$P o c = V o c^{2} / R$

Both Poc and Voc are giving so solve for R

$R = V o c^{2} / P o c = 5 V / 10 W = 2.5 O h m s$

To calclate the core inductance we will use the formular for apparent power.

$S^{2} = P^{2} + Q^{2}$

$S^{2} = | V o c * I o c^{*} |^{2}$

Subtituting in values and solving gives

$S^{2} = (5 V * 3 A)^{2} = 225 (V A)^{2}$

Use the apparent power and the real power to find the reactive power

$Q = \sqrt{S^{2} - P^{2}} = \sqrt{22 5^{2} - 1 0^{2}} = 224.8 V A r$

Finally

$Q = V o c^{2} / X$

Solve for the inductance

$Q = V o c^{2} / X$

$X = V o c^{2} / Q = 5 V^{2} / 224.8 V A r = 0.11 H$

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