The AC voltge and current in a house consists of two 120 V lines 180 o out of ph

Question

The AC voltge and current in a house consists of two 120 V lines  180o out of phase at a frequency of 60 Hz. A 240 V 2000 W dryer, a 240 V 4000 W hot water heater, a 120 V 1000 W television, and a 120 V 400 W refrigerator are running simultaneously?

Part A - Assuming that the price per kWhr is $0.10, what is the cost of running these appliances for 3 hours?

Part B - Assuming that at t = 0 the instantaneous current is 0 A, what is the instantaneous power at ?t?? = 1 ms?

Explanation / Answer

Total power = 2000 + 4000 + 1000 + 400 = 7400 W

(a) Cost of running these appliances = power x time x cost of electricity

= (7400/1000) x 3 x 0.1 = 2.2 $

(b) Instantenous power = I^2 R = ( (V/R)*sin( 2 pi f t ))^2 * R

= P * sin(2 pi f t )^2

Total instantenous power = ( 2000 + 4000 + 1000 + 400 ) * sin (2*pi*60*0.001) * sin (2*pi*60*0.001) = 1002.81 W

= 1003 W

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