1. If an RCL series circuit contains a resistance R= 266 omega, a capacitance C

Question

1. If an RCL series circuit contains a resistance R= 266 omega, a capacitance C = 4 mu F. and an inductance of L= 0.19 H, a) Calculate the inductive reactance X1. if the circuit is connected to a voltage source whose frequency is 350 Hz. b) Calculate the capacitive reactant Xc for the same conditions. c) Calculate the impedance / of the circuit at this frequency. d) lithe rms voltage across the generator is 151 V. calculate the average power p(at 350Hz), being used by the circuit. e) Calculate the resonant frequency f, of the circuit using the above values for R. L and C. I) Calculate the impedance Z of the circuit at resonance. g) If the rms voltage across the generator is 151 V when at resonance, calculate the average power P res being used by the circuit. 2. In the circuit shown. the AC voltage source supplies an rms voltage of 140 Vat frequency f. The circuit has R = 92 omega XL = 193 omega and XC = 100 omega a) Find the impedance of the circuit. b) Find the rms current flowing in the circuit. c) Find the phase angle in degrees between the current in the circuit and the voltage supplied by the AC source. d) At the instant the voltage across the generator is at its maximum value, what is the magnitude of the current in the circuit?

Explanation / Answer

1.a XL =wL =417.83ohms

b XC =1/wC =113.68ohms

c Z =R +j(XL-XC) =266+J304.14,

Magnitude of Z =404.05ohms

d Average power =Vrms*IrmsCos@ =151*0.373*0.658=37.13W

e frequency f =(1/2pi)Sqrt(1/LC) =183Hz

f imedance at resonant frequency becomes the resistance =R =266ohms

g average power at resonant frequency =Vrms*IrmsCos@ (since cos@ =1)

=151*(151/266) ( since at resonant frequency Z =R)

=85.72W

2.

a impedance Z =R +j(XL-XC)=92+J93

then the magniztude of Z =130.82ohms

b .Irms =Erms/Z =140/130.82 =1.07A

c.Phase angle =tan-1(XL-Xc/R) =45.30degrees

d.At resonance frequency instant only the current flow will be maximum

so the current at the resonant frequency =Vrms/R =140/92 =1.52A

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