Given the relationship, V 0 = i rms R , between the rms current through and the

Question

Given the relationship,

V0 =

irmsR,

between the rms current through and the maximum voltage across a resistor R, use the following information to determine the following quantities.

(a)    R = 100 , Vmax = 60 V, irms = ?
irms = A

(b)    R = 170 , irms = 2.5 A, Vmax = ?
Vmax = V

(c)    Vmax = 28 V, irms = 107 mA, R = ?
R =
d) Find the peak value of the current and the average power delivered in each case if a sinusoidal voltage of 30.0 V rms and a frequency of 80 Hz is applied to the following.
(a) a 80 resistor

iR, 0

PR, average

(b) a 0.1 H inductor

iL, 0

PL, average

(c) a 40.0 F capacitor

iC, 0

PC, average

PLEASE SHOW EVERY STEP AND EQUATION AND SAY WHAT IS THE FINAL ANSWER!!!

Explanation / Answer

(a)
R = 100 , Vmax = 60 V, irms = ?
Imax = Vmax/R
Imax = 60/100
Imax = 0.6 A

irms = imax/sqrt(2)
irms = 0.6/sqrt(2)
irms = 0.424 A

(b)
R = 170 , irms = 2.5 A, Vmax = ?
Vrms = Irms * R
Vrms = 2.5*170 V
Vrms = 425 V

Vmax = Vrms * sqrt(2)
Vmax = 425 * sqrt(2)
Vmax = 601.4 V

(c)
Vmax = 28 V, irms = 107 mA, R = ?
Imax = irms * sqrt(2)
imax = 107*sqrt(2) mA
imax = 151.32 mA

R = Vmax/imax
R = (28*10^3)/151.32
R = 185.0

(d)
(a)
R = 80
Imax = Vmax/R
Imax = 30*sqrt(2)/80
Imax = 0.43 A

Pav = Vrms^2/R
Pav = 30.0^2/80
Pav = 11.25 W

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