1) A coil of inductance 10^(-4) Henry and effective resistance 60 ohms is connected in parallel with a condenser of 10^(-10) Farad and the resonant circuit so formed is excited from an alternating current source. The frequency of this source is varied until the maximum impedance of the circuit is obtained. Determine the frequency of the generator when it happens.
The solution as given in my book is as follows:
In a parallel resonance circuit, the impedance of the circuit is maximum at the frequency of anti resonance and this frequency is given by
Frequency (f) = [(1/LC) – (R^2/L^2)]^(1/2)
I referred many books, but I didn’t come across the concept of anti resonance. But when I searched the internet, I found that the presence of non inductive resistance in A.C circuits along with inductor and capacitor, causes the resonance to be obtained at a frequency lower or higher than the frequency given by
f`=[1/(2(pi)][sqrt(LC)]
But I couldn’t understand how the above expression was obtained. Could someone please give an idea on how it could it obtained?

 

If you have not already discovered the tutorials section on this website here is a link to the section on that covers parallel tank circuits. The definition of anti-resonance is given.

hgmjr

 

From: http://www.butlerlabs.com/parallel_resonance.htm


"Parallel Circuit Resonance

In a parallel circuit containing equal XL and XC, the external circuit current is equal to that flowing through the parallel resistance. If the circuit contains no parallel resistance, the external current is zero. However, within a theoretical circuit consisting only of L and C and XL = XC, a large current called the "circulating current" flows, using no current from the power line. This occurs because the corresponding instantaneous values of the currents IL and IC always flow in opposite directions and, if these values are equal, no external circuit current will flow. This is called a "parallel resonant" circuit.

Because no external current flows in a resonant parallel circuit consisting only of L and C, the impedance at resonance is infinite, IL equals IC, and the total circuit current IT is zero. Since these effects are exactly opposite those of series resonance, parallel resonance is sometimes called "anti-resonance." Ohm's law for AC when applied to a parallel resonant circuit can be used to determine the value of the internal circulating current.

As in the case of a series resonant circuit, if either the frequency, inductive reactance or capacitive reactance of a circuit is varied and the two other values kept constant, the circuit current variation forms a resonance curve. However, the parallel resonance curve is the opposite of a series resonance curve. The series resonance current curve increases to a maximum at resonance then decreases as resonance is passed, while the parallel resonance curve decreases as resonance is passed.
"

The above excerpt taken from Basic Electricity Volume 4 pages 58-59, By Van Valkenburgh Nooger & Neville
Library of Congress Catalog Card No. 54-12946

 

To add to this discussion ... http://en.wikipedia.org/wiki/Electrical_resonance defines resonance as

Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedance between the input and output of the circuit is at a minimum (or when the transfer function is at a maximum).

This describes the series resonant circuit.

The parallel circuit is the antithesis of this definition, hence, anti-resonant.

 

Got your point guys.Thanks.