4 Standard North American house current is 120 V ac where th

4. Standard North American house current is 120 V ac, where the potential and current oscillate with a frequency of 60 Hz. What is the frequency of oscillation of the power consumed by a simple Ohm\'s Law resistor connected to this? Suggestion: look at Figure 18-22 in the text and think about how you would properly label its x-axis. Last resort: assume this 120V ac drives current through a 144 k resistor, and (using a spreadsheet) compute the power dissipated in the resistor every 30 s over the course of 0.018 s, graphing the result and then answer the question based on what you see there.

Solution

we can represent the Ac supply as

V =VoSin(2pift) where f = 60 Hz is the frequency of the AC supply

the load is pure resistive current

I = V/R = Vo/R Sin(2pift) is in phase with the voltage.

Io = Vo/R

Power P =IV = (Io² R/2) averaged over a complete cycle

frequency of the power is given by Sin²(2*pi*ft)

using the trignometric identity

Cos(2p) = 1-2Sin²(p)

we can write the frequency compnent of the power as

(1-Cos(2*2*pi*ft) )/2

or

1- Cos(2*pi*2ft)

the frequency of the power is doubled

= 120 Hz for the supply of 60 Hz.