Suppose there are two transformers between your house and the high-voltage trans

Question

Suppose there are two transformers between your house and the high-voltage transmission line that distributes the power. In addition, assume your house is the only one using electric power. At a substation the primary of a step-down transformer (turns ratio = 1:28) receives the voltage from the high-voltage transmission line. Because of your usage, a current of 39.2 mA exists in the primary of the transformer. The secondary is connected to the primary of another step-down transformer (turns ratio = 1:34) somewhere near your house, perhaps up on a telephone pole. The secondary of this transformer delivers a 240-V emf to your house. How much power is your house using? Remember that the current and voltage given in this problem are rms values.

Explanation / Answer

i2 = N1/N2 i1 = 21 * 47.8e-3 = 1.0038 A

i3 = N2/N3 i2 = 38 * 1.0038 = 38.1444 A

P = i3 V = 38.1444/2 * 240/2 = 38.1444 * 240/2 = 4577 W

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