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Question:

In the circuit shown, L=1μH, C=1μF and R=1kΩ. They are connected in series with an a.c. source V=V₀sinωt as shown. Which of the following options is/are correct?

The frequency at which the current will be in phase with the voltage is independent of R

At ω>>10⁶rad.s⁻¹, the circuit behaves like a capacitor

At ω≈0 the current flowing through the circuit becomes nearly zero

The current will be in phase with the voltage if ω=10⁴rad.s⁻¹

Solution:

Z=R+jωL−j/ωC
for ω₀=1√LC=10⁶ rad
Z=R for ω=ω₀
for ω<ω₀, (ωL−1/ωC)<0
Hence, Circuit is capacitive
for ω>ω₀, (ωL−1/ωC)>0
Hence, Circuit is Inductive
Hence, option A is wrong
B→ω≈0→Z→∞→i→0
Hence option B is correct
C→Current is in phase with voltage at resonance (ω=ω₀)
Hence Option C is wrong
D→ Resonant frequency ω₀=1√LC which is independent of R. Hence option D is correct.