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 6.00 V and a frequency of 25.0 kHz . The inductance in the circuit is 0.250 mH , the capacitance is 0.150 F , and the resistance is 2.60 .(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

Inductive reactance of the circuit,

XL =2*pi*f*L=2*pi*25*10^3*0.25*10^-3

XL =39.27 ohms

Capacitive reactance of the circuit,

Xc=1/(2pi*f*C)=1/(2pi*25*10^3*0.15*10^-6)

Xc=42.4 ohms

Impedance of the circuit,

Z=sqrt[R^2+(XL-Xc)^2]

Z=sqrt[2.6^2+(39.27-42.4)^2]

Z=4.07 ohms

total current

Irms =Vrms/Z = 6/4.07 =1.47 A

a)

Vab =I*XL =1.47*39.27

Vab = 57.73 V

b)

Vbc =I*XC =1.47*42.4

Vbc =62.33 V

c)

Vac =I(XL-Xc) =1.47(42.4-39.27)

Vac=4.6 V

d)

Vad =IZ =1.47*4.07

Vad =5.98 V

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