Q19 of 31 Page 267

Suppose the circuit in Exercise 18 has a resistance of 15Ω. Obtain the average power transferred to each element of the circuit, and the total power absorbed.

Given: Average power transferred to the resistor = 788.44 W

Average power transferred to the capacitor = 0 W


Power absorbed by the circuit = 788.44 W


Inductance L = 80 mH


In henry, Inductance L = 80 × 10-3H


Capacitance C = 60 μF = 60 × 10-6F


Resistance R = 15 Ω


Voltage V = 230 V


Frequency v = 50 Hz


Angular frequency is calculated as follows:


ω = 2πv


ω = 2 × 3.14 × 50(Hz) = 100π rad/s


The impedance can be calculated as follows:




On calculating, we get


Z = 31.728 Ω


Current can be calculated as follows: I = V/Z


I = 230 (A)/31.728 (Ω) = 7.25 A


The average power transferred to resistor can be calculated as follows:


Pr = I2R


Substituting values, we get


Pr = (7.25)2(A) × 15(Ω)


Pr = 788.44 W


The average power transferred to capacitor is equal to the average power transferred to resistor = 0


Total power absorbed = PR + Pc + PL = 788.4W


More from this chapter

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17

Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified in Exercise 11 for this frequency.

 18

A circuit containing a 80 mH inductor and a 60 μF capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.

(a) Obtain the current amplitude and rms values.


(b) Obtain the rms values of potential drops across each element.


(c) What is the average power transferred to the inductor?


(d) What is the average power transferred to the capacitor?


(e) What is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’.]

 20

A series LCR circuit with L = 0.12 H, C = 480 nF, R = 23Ω is connected to a 230 V variable frequency supply.

(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.


(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum


power.


(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?


(d) What is the Q-factor of the given circuit?

 21

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.