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 8.30 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 ? .

Part a)

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

Part B)

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

PartC)

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

Part D)

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

Explanation / Answer

a) Impedance of inductor coil, XL = 2 pi f L

XL = 2 x pi x 30 x 10^3 x 0.3 x 10^-3 = 56.55 ohm

Impedance of capacitor, Xc = 1 / (2 pi f C)

Xc = 1 / (2 x pi x 30 x 10^3 x 0.10 x 10^-6) = 53.05 ohm

total impedance of circuit, Z = R + j(XL - XC)

Z = 5 + j3.50

|Z| = sqrt(5^2 + 3.5^2) = 6.10 ohm

current through circuit = V/|Z| = 8.30 / 6.10 = 1.36 A

a) V = I |Z| = 1.36 x 56.55 = 76.94 Volt

b) V = 1.36 x 53.05 = 72.15 Volt

c) V = 1.36 x 5 = 6.8 Volt

d) V = 8.30 v

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