Sun November 04, 2012 By: Binshid Ummer

Explain these: 1.The impedance vector, in a vector-impedance diagram, is parallel to X-axis. The circuit is purely resistive,why 2.An a.c. circuit has a very small band width. The resistance of the circuit is low,How? 3.n electrical appliance of 120 ohms is connected to 220 V, 50 cycles a.c.? Calculate the average potential difference?

Expert Reply
Wed January 09, 2013
1. In this case pl mention which type of circuit is this, whether LCR OR LRetc.

The Q, quality factor, of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit correspondes to a more narrow bandwith, which is desirable in many applications. More formally, Q is the ration of power stored to power dissipated in the circuit reactance and resistance, respectively:

       Q = Pstored/Pdissipated = I2X/I2R
       Q = X/R
       where:      X = Capacitive or Inductive reactance at resonance
                   R = Series resistance.

This formula is applicable to series resonant circuits, and also parallel resonant circuits if the resistance is in series with the inductor. This is the case in practical applications, as we are mostly concerned with the resistance of the inductor limiting the Q. Note: Some text may show X and R interchanged in the “Q” formula for a parallel resonant circuit. This is correct for a large value of R in parallel with C and L. Our formula is correct for a small R in series with L.

A practical application of “Q” is that voltage across L or C in a series resonant circuit is Q times total applied voltage. In a parallel resonant circuit, current through L or C is Q times the total applied current.

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