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. In this circuit, the ac generator has an rms voltage of 6.00 V and a frequency of 32.0 kHz. The inductance in the circuit is 0.300 mH, the capacitance is 0.090 F, and the resistance is 2.50 ?. Let V be the reading on a voltmeter when it is connected between two different points on the circuit. (a) What is V between A and B? (b) What is V between B and C? (c) What is V between A and C? (d) What is V between A and D? http://www.webassign.net/walker/24-32.gif

Explanation / Answer

the steps to follow are: 1> find the current in the circuit 2>current* respective impedence = voltage across elements. Z= R + j(wL -1/(wC) ) Z= 2.5 + j(60.32 - 55.26) Z= 2.5 + j 5.06 Z= 5.64 angle(63.7 degree) current : I = V/Z = 1.064 angle(-63.7 degree) hence a) 1.064*(60.32)angle (90-63.7) =64.14 angle(26.3 deg) in rms = 45.35 V b) -55.26 angle(90deg ) * I = -58.79 angle(26.3 deg) in rms = -41.57 V c) voltage bet A and C is simply the addition of 1st 2 answers = 5.35 angle(26.3 deg) in rms =3.78 V d)V between A and D is simply V = 6 Volt

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