The figure shows an LCR Circuit with R = 40.0 ohm, L=185 mH, and C = 65.0 muF co

Question

The figure shows an LCR Circuit with R = 40.0 ohm, L=185 mH, and C = 65.0 muF connected to an ac source that generates a voltage given by: V(t) = 150 V Sin(100pit). (i) What is the maximum voltage generated by the source? (ii) What is the frequency of the ac source? (iii) What is the impedance Z of the circuit? (iv) What is the maximum current in the circuit? (v) Calculate the maximum potential drop V_r across the resistor, V_L inductor and V_c capacitor respectively (vi) What is the phase angle phi?

Explanation / Answer

1. Vmax= 150 V,

2.frequency w=2*pi*f= w/2pi

f= 100*pi/2pi= 50 Hz

3.impedance Z= sqrt (R2+(XL-XC)= sqrt (402+(wL-(1/wC))

Z = 40.1

4.Imax= Vmax/R= 150/40= 3.75 A

6. phase angle phi= tan-1((XL-XC)/R)= 12.7 degree

5. VR= IR= 3.75*40= 150 V

VL= I*XL= 217.8 V

VC= IXC= 182.13 V

=

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