An ac voltmeter, which displays the rms voltage between the two points touched b

Question

An ac voltmeter, which displays the rms voltage between the two points touched by its leads, is used to measure voltages in the circuit shown in the figure(Figure 1) . In this circuit, the ac generator has an rms voltage of 7.90 V and a frequency of 30.0 kHz . The inductance in the circuit is 0.300 mH , the capacitance is 0.100 F , and the resistance is 5.00

a) What is the reading on a voltmeter when it is connected to points A and B?

b) What is the reading on a voltmeter when it is connected to points B and C?

c) What is the reading on a voltmeter when it is connected to points A and C?

d) What is the reading on a voltmeter when it is connected to points A and D?

Explanation / Answer

w = 2*pi*f = 2*pi*30*10^3 = 188.49*10^3 rad/s

XL = wL = 188.49*10^3*0.30*10^-3 = 56.54 ohm

XC = 1/wC = 1/(188.49*10^3*0.10*10^-6) = 53.05 ohm

R = 5.0 ohm

TOTAL IMPEDENCE OF THE CIRCUIT Z = [R^2 + (XL -XC)^2]^0.5

=> Z = [25 + 12.18]^0.5 = 6.097 ohm

a) voltage across points A and B

V = XL*7.90/Z = 56.54*7.90/6.097 = 73.259 volt

b) voltage across points B and C

V = XC*7.90 / Z = 53.05*7.90/6.097 = 68.73 volt

c) voltage across points A and C

V = (XL -XC)*7.90/Z = 3.49*7.90/6.097 = 4.522 volt

d) voltage across points A and D

V = generator voltage = 7.90 volt

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