Answer :

(a) Given: L = 0.12 H


C = 480 nF


Converting into Farad, we get 480 × 10-9F


R = 23Ω


Voltage = 230 V


Peak voltage can be calculated as follows:


V0 = √2V


Substituting values we get


V0 = 230√2


V0 = 325.22 V


Current flowing through the circuit is given by the following:


I0 =


At resonating frequency, ωR L - 1/ωRC = 0


ωR = 1/√LC


= 1/ √0.12 (H) × 480 × 10-9 (F) = 4166.67 rad/s


Resonant frequency can be calculated using the formula:


vR = ωR/2π


vR = 4166.67(Hz)/2 × 3.14


vR = 663.48 Hz


Maximum current is calculated as follows:


(I0)max = V0/R = 325.22(Hz)/23 = 14.14 A


(b) The maximum power absorbed by the circuit can be calculated as follows:


Pav = 1/2(I0)2maxR


Substituting the values, we get


Pav = 1/2 × (14.14)2(A) × 23 (Ω)


Pav = 2299.33 W


Therefore, the resonating frequency is 663.48 Hz.


(c) The power transferred is equal to the half of the power at the resonating frequency.


Frequency at which power is half = ωR �∆ω


Or = 2π (vR �∆v)


Where ∆ω = R/2L


Substituting the values we get


∆ω = 23/2(Ω) × 0.12(H)


∆ω = 95.83 rad/s


Therefore, change in frequency is written as follows:


∆v = 1/2π × ∆ω


Substituting the values, we get


∆v = 95.83(rad/s)/2π = 15.26 Hz


vR + ∆v is calculated as follows:


663.48(Hz) + 15.26(Hz) = 678.74 Hz


vR-∆v is calculated as follows:


663.48(Hz) – 15.26(Hz) = 648.22 Hz


The current amplitude is calculated as follows:


I’ = 1/√2 × (I0)max


I’ = 14.14(A)/ √2


I’ = 10 A


(d) Q factor can be calculated as follows:


Q = ωRL/R


Q = (4166.67 rad/s) × 0.12H/23Ω


Q = 21.74


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