..il AT&T; 5:42 PM session.masteringphysics.com Problem 24.53 MasteringPhysics P

Question

..il AT&T; 5:42 PM session.masteringphysics.com Problem 24.53 MasteringPhysics Problem 24.53 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 Q Tap image to zoom In this circuit, the ac generator has an rms voltage of 6.50 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 3.10 Part A What is the reading on a voltmeter when it is connected to points A and B? Express your answer using two significant figures. Give Up

Explanation / Answer

Inductive reactance

XL=2pifL=2pi*(25*103)*(0.25*10-3)=39.27 ohms

Capacitive reactance

Xc=1/2pifC =1/2pi*(25*103)*(0.15*10-6)=42.44 ohms

Impedance

Z=sqrt[R2+(XL-XC)2]=sqrt[3.12+(39.27-42.44)2]

Z=4.4348 ohms

Rms Current

I=V/Z=6.5/4.4348 =1.4657 A

a)

VAB=IXL=1.4657*39.27=57.55 Volts

b)

VBC =IXC=1.4657*42.44=62.2 Volts

c)

VCD=IR=1.4657*3.1=4.54 Volts

d)

V=sqrt(VR2+(VL-VC)2]=6.5 Volts

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