Question

(a) Derive an expression for the average power

consumed in a series LCR circuit connected to

ac source in which the phase dierence between

the voltage and the current in the circuit is f.

(b) Dene the quality factor in an ac circuit.

Why should the quality factor have high value

in receiving circuits? Name the factors on which

it depends.

Answer 1

ANSWER:

A) The average power consumed in a series LCR circuit is VrIrcosФ

Explanation :

Let the voltage in the circuit,

v = Vsinwt

and the current in the circuit,

i = Isin(wt-Ф)

Hence total work done in a complete cycle,

W = \int\limits^T_0 {vi} \, dt

0∫T

vidt

=> W = ∫ Vsinwt . Isin(wt-Ф) dt

solving this we get,

W = VIT cosФ/2

we know that power is defined as the work done per unit time,

=> P = W/T = VI cosФ/2

=> P = V/√2 x I/√2 x cosФ

=> P = VrIrcosФ

where Vr and Ir are the rms values respectively.

B) The ratio

ω0L/R is called the quality factor or Q-factor.

Q = ω0L/R

The quality factor has high value in receiving circuits in order to get a sharp gain for the desired channel frequency.

The quality factor depends on the values of the following:

1. Inductance
2. Resistance
3. Capacitance

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