Electromagnetic Induction and Alternating Current 7 Question 21

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

(2017 Adv.)

(a) At ω0, the current flowing through the circuit becomes nearly zero

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

(c) The current will be in phase with the voltage if ω=104rads1

(d) At ω106rads1, the circuit behaves like a capacitor

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Answer:

Correct Answer: 24. (a, b)

Solution:

  1. At ω0,XC=1ωC=. Therefore, current is nearly zero.

Further at resonance frequency, current and voltage are in phase. This resonance frequency is given by

ωr=1LC=1106×106=106rad/s

We can see that this frequency is independent of R.

Further, XL=ωL,XC=1ωC

At, ω=ωr=106rad/s,XL=XC.

For ω>ωr,XL>XC. So, circuit is inductive.



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