Help me calculate the question which I have kept getting wrong. (These are the a

Question

Help me calculate the question which I have kept getting wrong.

(These are the answers I have entered which are wrong: 144.9, 145.0, 142.3, 142.2.)

A capacitor, a co and two resistons of equal resistance are arranged in an AC circuit as shown in the figure below. An AC source provides an emf of AVrms 17.0 V at a frequency of 60.0 Hz. When the double-throw switch S is open as shown in the figure, the rms current is 188 mA. When the switch is closed in position a, the rms current is 309 mA. When the switch is closed in position b, the rms current is 137 mA. H AV Inns (a) Determine the possible values of R. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) 81.7 none (b) Determine the possible values of C. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) HF 28.72 HF none (c) Determine the possible values of L. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out a intermediate results to at least four-digit accuracy to minimize roundoff error. mH 347.8 m H (d) Is more than one set of values possible for R? Yes O No

Explanation / Answer

let capacitive reactance is -j Xc and inductive reactance is j Xl.

when switch is open, rms current=Vrms/total impedance magnitude

=17/sqrt(R^2+(Xl-Xc)^2)

==>0.188=17/sqrt(R^2+(Xl-Xc)^2)

==>R^2+(Xl-Xc)^2=8176.8....(1)

when switch is closed in b,

L is shorted.

==>0.137=17/sqrt(R^2+Xc^2)

==>R^2+Xc^2=15397.73 ....(2)

when switch is closed in position a, resistance becomes R/2 (as R is in parallel with R)

so 0.309=17/sqrt((R/2)^2+(Xl-Xc)^2)

==>(R/2)^2+(Xl-Xc)^2=3026.8...(3)

subtracting equation 3 from equation 1:

(3/4)*R^2=5150

==>R=82.865 ohms

using this value of R in equation 2,

Xc=92.364 ohms

using this value of R and Xc in equation 1,

(Xl-Xc)^2=8176.8-R^2=1310.168

==>Xl-Xc=36.1962 or Xc-Xl=36.1962

using Xc=92.364,

Xl=128.56 ohms

or Xl=56.1678 ohms

as Xl=2*pi*frequency*L

==>L=Xl/(2*pi*60)

for Xl=128.56, L=128.56/(2*pi*60)=0.341 H

for Xl=56.1678 ohms, L=0.149 H

so you can enter the value 149 mH as the second answer.

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