Question

what is the impedance of an ideal parallel resonant circuit without resistance in either branch ?
a) zero
b) inductive
c) capacitive
d) infinite​​

Answer 1

Given : an ideal parallel resonant circuit without resistance in either branch

To Find : impedance

a) zero

b) inductive

c) capacitive

d) infinite​

Solution:

Similar to  a Series RLC circuit in Parallel RLC circuit also Resonance occur when f = 1/2π√LC

At resonance the parallel LC  circuit acts like an open circuit

Hence  circuit current being determined by the resistor, R only.

Total impedance of a parallel resonance circuit at resonance is just the value of the resistance in the circuit

Hence Z = R

R = Resistance

Z is impedance

an ideal parallel resonant circuit without resistance

Hence R = 0

=> Z = 0

impedance of an ideal parallel resonant circuit without resistance in either branch is ZERO

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Answer 2

${ \red{ \bf{ Given: }}}$

An ideal parallel resonant circuit without resistance in either branch.

${ \red{ \bf{ To\: Find: }}}$

Impedance

${ \blue{ \bf{ a)\: zero }}}$

${ \blue{ \bf{ b)\: inductive}}}$

${ \blue{ \bf{ c)\: capacitive }}}$

${ \blue{ \bf{ d)\: infinite }}}$

${ \red{ \bf{ Solution: }}}$

Similar to a Series RLC circuit in Parallel RLC circuit also Resonance occur when f = 1/2πVLC

At resonance the parallel LC circuit acts like an open circuit

Hence circuit current being determined by the resistor, R only.

Total impedance of a parallel resonance circuit at resonance is just the value of the resistance in the circuit

${ \green{ \bf{ Hence\: Z = R }}}$

${ \green{ \bf{ R \:= \:Resistance }}}$

${ \green{ \bf{ Z\: is \:impedance }}}$

an ideal parallel resonant circuit without resistance

${ \green{ \bf{Hence\: R = 0 }}}$

${ \green{ \bf{ => Z = 0 }}}$

Impedance of an ideal parallel resonant circuit without resistance in either branch is

${ \orange{ \bf{ZERO }}}$