A resistor with R = 3.0k is connected to an AC generator that operates at 60 Hzw

Question

A resistor with R = 3.0k is connected to an AC generator that operates at 60 Hzwith an amplitude of 37 V. (a) Find the amplitude of the current throughthe resistor.
1 A

(b) Find the maximum instantaneous power dissipated in theresistor.
2 W

(c) Find the minimum instantaneous power dissipated in theresistor.
3 W

(d) Find the average power dissipated in the resistor.
4 W

(e) How long will it take this resistor to dissipate 190 J?
5 s

(a) Find the amplitude of the current throughthe resistor.
1 A

(b) Find the maximum instantaneous power dissipated in theresistor.
2 W

(c) Find the minimum instantaneous power dissipated in theresistor.
3 W

(d) Find the average power dissipated in the resistor.
4 W

(e) How long will it take this resistor to dissipate 190 J?
5 s

Explanation / Answer

(a) Find the amplitude of the current throughthe resistor.
I= V/R I= 37/3.0x103 =0.0123 A

(b) Find the maximum instantaneous power dissipated in theresistor.
P=IV P=0.456 W

(c) Find the minimum instantaneous power dissipated in theresistor.
P= 0 W at V(t)=0 I(t) =0 therefore P(t)=0

(d) Find the average power dissipated in the resistor.
P=Vrms2/R P= (2/2 37)2 /3.0x103 P= 0.0087 W

(e) How long will it take this resistor to dissipate 190 J?
Since P=Energy/time Energy = 190 / 0.0087 = 21,786 s

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