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Resonance In Series LCR Circuit MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Resonance in Series LCR circuit is considered one the most difficult concept.

  • 18 Questions around this concept.

Solve by difficulty

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In a  LCR circuit capacitance is changed from C to 2C . For the resonant frequency to remain unchanged, the inductance should be changed from L to

In a series resonant LCR circuit, the voltage across R is 100 volts and R = 1 k \Omega with C = 2 \mu F. The resonant frequency \omega is 200 rad/s. At resonance the voltage across L is

In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1µF and resistance R is 100 \ \Omega . The frequency at which resonance occurs is?

The resonance frequency of the tank circuit of an oscillator when L=10π2mH and C=0.04μ F are connected in parallel is:

Concepts Covered - 1

Resonance in Series LCR circuit

Resonance in Series LCR circuit-

As we have discussed that when- 

     

ωL=1ωC

then tanφ is zero i.e. phase angle (φ) is zero and voltage and current are in phase. We have called it electric resonance. So, if XL=XC, then the equation of impedance become -

Z=R2+(ωL1ωC)2=R


So, we get minimum value of Z.
In this case impedance is purely resistive and minimum and currents has its maximum value. Now as -

ωL=1ωC


So,

ω=1LC


As, ω=2πfo. Where fo is the frequency of applied voltage.

                                   

                                                                So,

                                                                           

fo=12πLC


This frequency is called resonant frequency of the circuit.
Peak current in this case is given by -

io=VoR
 

We will now discuss about the resonance curve and its nature. We will show the variation in circuit current (peak current i0) with change in frequency of the applied voltage - 

                                   

This figure/graph shows the variation of current with the frequency. 

Conclusions from the graph - 

1. If R has small value, the resonance is sharp which means that if the applied frequency is lesser to resonant frequency f0,the current is high otherwise

2. If R is large, the curve is broadsided which means that those is limited change in current for resonance and non-resonance conditions

                  

Note -                                

The natural or resonant frequency is Independent from the resistance of the circuit.

XL=Xc=ω0L=1ω0cν0=12πLc(Hz)
 

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Resonance in Series LCR circuit

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