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 8.50Vand a frequency of 30.0kHz . The inductance in the circuit is 0.300mH , the capacitance is 0.100?F , and the resistance is 2.80? .

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

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

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

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

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 8.50Vand a frequency of 30.0kHz . The inductance in the circuit is 0.300mH , the capacitance is 0.100?F , and the resistance is 2.80? . What is the reading on a voltmeter when it is connected to points A and B? What is the reading on a voltmeter when it is connected to points B and C? What is the reading on a voltmeter when it is connected to points A and C? What is the reading on a voltmeter when it is connected to points A and D?

Explanation / Answer

Impedences:

Zr = 2.80 ohm

Zc = 1/wc = 1/(2pi30000x0.1?F ) = 53.07 ohm

ZL = wL = 56.52 ohm

Z = 2.80 + j(56.52 - 53.07) = 2.80 + j3.45

i = 8.50/sqrt(2.80^2 + 3.45^2) = 1.91 A

1) V = iZL

2)V =i(-Zc)

3)V = i(ZL - Zc)

4)V =i(sqrt(Zr^2 + (ZL - Zc)^2)) = 8.50

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