A resistor R = 15 ft is connected to an AC voltage supply with a frequency f = 0

Question

A resistor R = 15 ft is connected to an AC voltage supply with a frequency f = 0.25 Hz and rms voltage V_rms = 6V. A) Calculate the squareroot-mean-squared current I_rms. B) Calculate the peak voltage and current V_R and I_R. C) What is the period of oscillation? D) Calculate the average power dissipated by the resistor P_R E) On the left graph, draw the instantaneous voltage V_R(t) and current i_R(t), beginning with both at the maximum values at 0 s (from the left). F) On the right graph, draw the instantaneous power loss P_R(t), and indicate the average power P_R with a horizontal line.

Explanation / Answer

a)

Irms=Vrms/R =6/15

Irms=0.4 A

b)

Peak Voltage

VP=sqrt[2]*Vrms=8.485 Volts

Peak current

IP=sqrt[2]*Irms=0.567 A

c)

Time period

T=1/f =1/0.25

T=4 s

d)

Average power

Pav=Irms2R=0.42*15

Pav=2.4 W

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