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 that your house is the only one using electric power. At a substation the primary coil 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 47.6 mA exists in the primary coil of this transformer. The secondary coil is connected to the primary of another step-down transformer (turns ratio = 1:36) somewhere near your house, perhaps up on a telephone pole. The secondary coil of this transformer delivers a 220-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

solution: 1st Step down:- we knw that Vp/Vs = Np/Ns = Is/Ip =>28/1 = Is/47.6 x 10^-3) =>Is = 28 x 47.6x 10^-3 = 1.33 amp 2nd Step down:- Vp/Vs = Np/Ns = Is/Ip => 36/1 = Is/1.33 =>Is = 36 x 1.33 = 45.22 amp Thus the power consumption by P = V x i = 220*47.6 = 10400.6 J = 10400.6 J

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