Five infinite-impedance voltmeters, calibrated to read rms values, are connected

Question

Five infinite-impedance voltmeters, calibrated to read rms values, are connected as shown in figure (Figure 1) . Let R=200, L=0.400 H, C=6.00 F and V=30.0 V. I have done parts A-E and have written them below. All I need is help with parts F-J.

A) What is the reading of the voltmeter V1 if =200rad/s? Answer V1= 5.44 V

B) What is the reading of the voltmeter V2 if =200rad/s? Answer V2= 2.18 V

C) What is the reading of the voltmeter V3 if =200rad/s? Answer V3= 22.7 V

D) What is the reading of the voltmeter V4 if =200rad/s? Answer V4= 20.5 V

E) What is the reading of the voltmeter V5 if =200rad/s? Answer V5= 21.2 V

F) What is the reading of the voltmeter V1 if =1000rad/s?

G) What is the reading of the voltmeter V2 if =1000rad/s?

H) What is the reading of the voltmeter V3 if =1000rad/s?

I) What is the reading of the voltmeter V4 if =1000rad/s?

J) What is the reading of the voltmeter V5 if =1000rad/s?

Explanation / Answer

if w = 1000 rad/s

impedence of circuit,

Z = sqrt (R^2 + (wL - 1/wC)^2)

Z = 307.31 ohm

maximum current lmax = V / Z

lmax = 30 / 307.31 =0.0976 A

lrms = 0.0976 / sqrt(2) = 0.069 A

(F)

V1 = lrms*R = 0.069*200

V1 = 13.8 V

(G)

V2 = lrms*xL = lrms*w*L

V2 = 0.069*1000*0.4

V2 = 27.62 V

(H)

V3 = lrms*1 / wC = 0.069 / 1000*6*10^(-6)

V3 = 11.5 V

(l)

V4 = V3 - V2

V4 = -16.2 V

(J)

V5 = Vrms

V5 = 30 / sqrt(2)

V5 = 21.2 V

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