1 An ac voltmeter, which displays the rms voltage between the two points touched

Question

1 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 ms voltage of 16.00 V and a frequency of 15.0 k. C.. 65nF, C: 45 nF, Ri = 7.53 ' R: 6.55 . (a) What should be the inductance of the col that sets the circuit to resonate with the power supply? (b) What is the power delivered by the power supply? Now, the ac power generator is set to 48.0 V and frequency, f-50.0 kHz; A coil of L- 0.35-mH inductance is connected between A and B, a capacitor having a 42.0-nF capacitance between B and C, and a resistor with a resistance of 55.0-2 between C and D. (c) Calculate the voltage across the coil, VAB, (d) across the capacitance, Vec, (e) across the resistor, Va, and ( the voltage between A and D, VAD (9) What is the power supplied by the circuit? (h) What should the frequency of the power supply be so that it will be at resonance with the circuit? () Deduce the current at resonance.

Explanation / Answer

Inductive reactance

XL=2pifL=2pi*50000*(0.35*10-3) =109.956 ohms

Capacitive reactance

XC=1/2pifC =1/2pi*50000*(42*10-9)=75.8 ohms

Impedance

Z=sqrt[552+(109.956-75.8)2]=64.75 ohms

Current

I=V/Z =48/64.75=0.7413 A

Power factor

Cos(o) =R/Z =55/64.75 =0.8494 A

f)

Voltage between A and D is

VAD=48 Volts

g)

Power supplied by the circuit

P=VICos(o)=48*0.7413*0.8494 =30.22 Watts

h)

f=1/2pisqrt(LC) =1/2pisqrt[0.35*10-3*42*10-9]

f=41511 Hz or 41.511 KHz

i)

I=V/R =48/55=0.8727 A

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