Alternating Current

JEE Main level, single correct, medium

97 of 190

Question 97 of 190

For a series LCRLCR circuit, II vs ω\omega curve is shown

(a) To the left of
ωr{\omega }_{r}, the circuit is mainly capacitive.
(b) To the left of
ωr{\omega }_{r}, the circuit is mainly inductive.
(c) At
ωr{\omega }_{r}, impedance of the circuit is equal to the resistance of the circuit.
(d) At
ωr{\omega }_{r}, impedance of the circuit is 00.
Choose the most appropriate answer from the options given below.

Show answer and solution

Answer: (C) (a) and (c) only

The impedance of an AC circuit is given by, Z=R2+(XC−XL)2Z=\sqrt{{R}^{2}+{\left({X}_{C}-{X}_{L}\right)}^{2}}.
For current to be maximum
ZZ should be minimum. The value of ZZ will be minimum when XC−XL=0{X}_{C}-{X}_{L}=0. Therefore, the value of Z=RZ=R. Hence, statement C is correct and statement D is wrong.
To the left of
ωr{\omega }_{r} i.e. when ω<ωr\omega \lt {\omega }_{r}, XC>XL{X}_{C}\gt {X}_{L}. Therefore, the circuit is mainly capacitive. Hence, statement A is correct and statement B is wrong.

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