Let us consider an .alternating source connected across an inductance L in parallel with a capacitor C. The resistance in series with the inductance is R and with the capacitor is zero.
Let the instantaneous value of emf applied be V and the corresponding current is I, IL and I0 Then,
I = IL +IC
The magnitude of the admittance,
The admittance will be minimum, when
It gives the condition of resonance and the corresponding_ frequency,
is known as resonance frequency. At resonance frequency admittance is minimum or the impedance is maximum. Thus, the parallel circuit does not allow this frequency from the source to pass in the circuit Due to this reason the circuit with such a frequency is known as rejector circuit.
If R = 0, resonance frequency is 1/2Π same as resonance frequency in series circuit.
At resonance, the reactive component of Y is real. The reciprocal of the admittance is called the parallel resistor or the dynamic resistance. The dynamic resistance thus, reciprocal of the real part of the admittance.
Dynamic resistance =
Substituting =
we have, dynamic resistance =
.. peak current through, the supply =
The peak current through capacitor =
The ratio of the current through capacitor and through the supply is known as Q-factor
This is basically measure of current magnification the rejector circuit at resonance exhibit current magnification of ωL/R similar to the voltage magnification of same ratio exhibited by the accepter circuit at resonance
At resonance the current through the supply and voltage are in phase, while the current through the capacitor leads the voltage by 9O°
Illustration 5 : For the circuit show in figure. Current in inductance is 0.8 A while in capacitance is 0.6 A., What ‘is the, current drawn’ from. the source? .
Solution : In this a circuit ε=εο sinωt applied across an inductance and capacitance in Parallel, current in inductance will lag the applied voltage while across the capacitor will lead,