Question

The value of admittance at resonance in antiresonant is.
(B) $\sqrt {{G^2} - {S^2}} $
(B) ${G^2} + {S^2}$
(C)$\sqrt {{G^2} + {S^2}} $
(D)$\dfrac{{{G^2}}}{{{S^2}}}$

Answer 1

Hint: Admittance is inverse of impedance so you need to find impedance at resonance in antiresonant condition and in antiresonant condition impedance approaches infinity and the circuit contains a capacitor and coil in parallel.

Complete step by step answer:
We know that, admittance is inverse of impedance(Z)
So $Y = \dfrac{1}{Z}$ where Y is admittance.
For a circuit with capacitor and a coil in parallel inverse of impedance(Z) is,
$\dfrac{1}{Z} = G + Sj \Rightarrow Y = G + Sj$ where, G is resistance and S is reactance(Resistance due to capacitor and inductor)
Since G and S are perpendicular so the total magnitude of admittance(Y) will be the square root of the sum of squares of G and S.
i.e; $\left| Y \right| = \sqrt {{G^2} + {S^2}} $

Hence Option-C is correct.

Note: In antiresonant condition since capacitor and coil are in parallel calculating impedance is hard as it involves a lot of reciprocals so admittance is defined for easier calculation and you need to simply put formula to get the answer.