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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?

640514_d7d8d01883fa4b5ba57ce8a591632f7f.png
  1. At ω0 the current flowing through the circuit becomes nearly zero
  2. At ω>>106rad.s1, the circuit behaves like a capacitor
  3. The current will be in phase with the voltage if ω=104rad.s1
  4. The frequency at which the current will be in phase with the voltage is independent of R

A
The current will be in phase with the voltage if ω=104rad.s1
B
At ω>>106rad.s1, the circuit behaves like a capacitor
C
The frequency at which the current will be in phase with the voltage is independent of R
D
At ω0 the current flowing through the circuit becomes nearly zero
Solution
Verified by Toppr

Z=R+^jωLjωC
for ω0=1LC=106 rad
Z=R
for ω<ω0, (ωL1ωC)<0
Hence, Circuit is capacitive
for ω>ω0, (ωL1ωC)>0
Hence, Circuit is Inductive
Hence, option A is wrong
B>ω0Z>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=1LC
which is independent of R. Hence option D is correct.

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