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?

P(t=1ms)= 7607W    P(t=1ms)= 11584W    P(t=1ms)= 596W    P(t=1ms)= 1193W    P(t=1ms)= 5792W    P(t=1ms)= 1003W    P(t=1ms)= 2006W    P(t=1ms)= 3632W    P(t=1ms)= 3804W    P(t=1ms)= 1816W    P(t=1ms)= 12794W    P(t=1ms)= 6397W  

Explanation / Answer

Part-A : Assuming that the price per kWhr is $0.1, then the cost of running these appliances for 3 hours which is given as -

Total power of following appliances, Ptotal = Pdryer + Pheater + Ptelevision + Prefrigerator

Ptotal = (2000 W) + (4000 W) + (1000 W) + 400 W)

Ptotal = 7400 W

Energy may be defined by,   E = Ptotal x time

where, t = 3 hr

E = (7400 W) x (3 hr)

E = 22200 Whr

E = 22.2 kWhr

cost price is given as :

cost = E x $0.1

cost = ( 22.2 kWhr) x ($0.1 / kWhr)

cost = $ 2.22

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