Question

In a series LCR circuit, obtain the conditions under which (i) the impedance of the circuit is minimum and (ii) watt-less current flows in the circuit.

Answer 1

(i) The impedance of a series LCR circuit is given by will be minimum when ωL=1/ωC, i.e., when the circuit is under resonance. Hence, for this condition, Z will be minimum and will be equal to R.

(ii) Average power dissipated through a series LCR circuit is given by Pav=EvIvcosϕ where, Ev = rms value of alternating voltage Iv = rms value of alternating current Φ = phase difference between current and voltage For wattless current, the power dissipated through the circuit should be zero. i.e., cosϕ=0⇒ϕ=π2 Hence, the condition for wattless current is that the phase difference between the current and voltage should be π/2 and the circuit is purely inductive or purely capacitive.

See attachment

Answer 2

Hey !!

(i) he impedance of a series LCR circuit is give by,

    Z = √R² + (Xl - Xc)²

or For Z to be minimum, Xl = Xc (or ω = 1/√LC)

(ii) For wattless current to flow, circuit should not have any ohmic resistance, R = 0

ALTERNATIVELY

Power = Vrms Irms cosΦ

POWER = 0

∴ Wattless current flows when the impedance of the circuit is purely inductive/capacitive or the combination of the two.

GOOD LUCK !!