Derive the formula for resonant frequency of the circuit with a pure capacitor in parallel with a coil having resistance and inductance. Find the expression for dynamic resistance of this parallel resonant circuit.
Consider a parallel circuit consisting of a coil and a capacitor as shown below. The impedances of two branches are:-
Admittance of the circuit `overline(Y)=overline(Y_1)+overline(Y_2)`
`overline(Y)=(R-jX_L)/(R^2+X_L^2)+j/X_C = R/(R^2+X_L^2)-j(X_L/(R^2+X_L^2)-1/X_C)`
At resonance the circuit is purely resistive. Therefore, the condition for resonance is.
Where 𝑓0 is called as the resonant frequency of the circuit.
If R is very small as compared to L then
DYNAMIC IMPEDANCE OF A PARALLEL CIRCUIT.
At resonance the circuit is purely resistive the real part of admittance is `R/(R^2+X_L^2)`.Hence the dynamic impedance at resonance is given by,
At resonance ,