NEET Previous Year Papers’ Analysis: LCR Circuits, Concepts And Solutions

NEET Previous Year Papers’ Analysis: LCR Circuits, Concepts And Solutions

Edited By Safeer PP | Updated on May 31, 2022 08:57 AM IST | #NEET

The National Eligibility Cum Entrance Test (NEET) Paper has questions from Physics, Chemistry and Biology. The weight of Physics is 25% of total marks. As NEET is highly competitive, each subject is important. Most of the NEET students find Physics difficult. But enough practice and clarity in concepts can make Physics easy for students. Each chapter of the Physics syllabus for NEET is important. Here is the analysis of the Class 12 chapter Alternating Current and explanations on concepts and questions of the topic, Alternating Current, the LCR circuits.

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NEET Previous Year Papers’ Analysis: LCR Circuits, Concepts And Solutions
NEET Previous Year Papers’ Analysis: LCR Circuits, Concepts And Solutions

In the last six years' paper of NEET there were 8 questions from AC circuits and out of these five questions were associated with the series LCR circuit. There were two questions from AC circuits in NEET 2021 in which one question was of LCR series circuit and another a combination of the concept of LCR circuit and series resonance. It shows that AC circuits and the concepts of LCR series circuits are important for NEET examination. JEE Main also has a number of questions from the LCR circuits. Let us have a look at the LCR series circuit.

LCR Series Circuit

1653630750417

R, L and C are connected in series across an ac voltage source. The current may lead or lag the voltage depending on the values of resistance and inductive and capacitive reactance by some angle ɸ. The calculation of ɸ is discussed later.

Force Voltage Analogy

Applying Kirchoff's voltage Law to the given RLC series circuit we get

\\V_s-V_R-V_L-V_C=0\\V_s=IR+L\frac{di}{dt}+\frac{1}{C}\int idt\\or\\V_s=L\frac{d^2q}{dt^2}+R\frac{dq}{dt}+\frac{q}{C}------(1)

The equation of damped or forced oscillator(Studied in the chapter, Oscillation of Class 11) is

F=m\frac{d^2x}{dt^2}+B\frac{dx}{dt}+Kx------(2)

Comparing (1) and (2) the inductance L is analogous to mass m, resistance R is analogous to frictional coefficient B and capacitance is analogous to the 1/K where K is the spring constant.

Force Voltage Analogy

Mechanical Quantity

Electrical Quantity

Force

Voltage

Velocity

Current

Displacement

Charge

frictional coefficient

Resistance

Mass

Inductance

Spring constant

1/Capacitance

Question (JEE Main 2020)

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be?

  1. L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m

  2. L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b

  3. L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b

  4. L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}

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Option c) is the right answer.

Phasor Diagram Of Series RLC Circuit

Phasor diagram for VL>VC

1653630753171

Phasor diagram for VC>VL

1653630754041

ɸ is the phase difference(angle between the resultant voltage and the current)

Resultant Voltage Of LCR Series Circuit

1653630747928

Question (JEE Main 2014)

When the RMS voltages VL, VC and VR are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio VL: VC: VR = 1:2:3. If the RMS voltage of the AC source is 100 V, then VR (in V) is close to

Solution:

\\Given\\100=\sqrt{V_R^2+(V_L-V_C)^2}

From the given ratio

\\V_C=\frac{2}{3}V_R\ And \ V_L=\frac{1}{3}V_R

\\So,\\100=V_R\sqrt{1+\left ( \frac{1}{3}-\frac{2}{3}  \right )^2}\\100=\frac{\sqrt{10}}{3}V_R\\V_R=30\sqrt{10}=94.86V

Impedance Z Of LCR Series Circuit

Z=\sqrt{R^2+(X_L-X_C)^2}

As XL=⍵L and XC=1/(⍵C), the impedance can be calculated as

Z=\sqrt{R^2+\left (\omega L-\frac{1}{\omega C}\right )^2}

Impedance Triangle

1653630749757

From the impedance triangle the angle phi can be calculated using trigonometric functions.

1653630748514

That is cosɸ=R/Z and cosɸ is known as the power factor.

tan\phi=\frac{|X_L-X_C|}{R}

sin\phi=\frac{|X_L-X_C|}{Z}

Question(JEE Main 2017)

A sinusoidal voltage of peak value 283 V and angular frequency (⍵) as 320 rad/s is applied to a series LCR circuit. Given that R=5 Ω, L=25 mH and C=1000 µF. The total impedance and phase difference between the voltage across the source and the current will be:

Solution:

Impedance

Z=\sqrt{R^2+(X_L-X_C)^2}

X_{L} =\omega L = (2\pi f) L = 320\times25\times 10^{-3}\Omega=8\Omega

X_{C} = \frac{1}{\omega C} = \frac{1}{320\times10^{-3}} \Omega = \frac{1}{0.32}\Omega=3.125\Omega

Z=\sqrt{5^2+(8-3.125)^2}=6.98\Omega

The phase difference between the voltage across the source and the current

\phi=cos^{-1}\frac{R}{Z}=cos^{-1}\frac{5}{6.98}\approx 45^0

Power In An AC Circuit

Instantaneous Power

It is the product of instantaneous voltage and current. That is:

\\p=V_msinwtI_msin(wt-\phi)\\

Using the trigonometric relation

sinasinb=\frac{1}{2}(cos(a-b)-cos(a+b))

p=\frac{1}{2}V_mI_m(cos\phi-cos(2wt-\phi))

Average Power

Voltage and current are not constant in an AC circuit, they change with respect to time. So power also changes. So the average power over a period T is

\\P_{avg}=\frac{1}{T}\int_{0}^{T}vidt

Where vi is the instantaneous power

\\P_{avg}=\frac{1}{T}\int_{0}^{T}vidt

\\P_{avg}=\frac{1}{T}\int_{0}^{T}\frac{1}{2}V_mI_m[cos\phi-cos(2wt-\phi)]dt\\\int_{0}^{T}cos(2wt-\phi)dt=0\\So\ P_{avg}=\frac{V_mI_m}{2}cos\phi\\ P_{avg}=\frac{V_m}{\sqrt{2}}\frac{I_m}{\sqrt{2}}cos\phi=V_{rms}I_{rms}cos\phi

Where cosɸ is known as the power factor.

Average power is measured in Watts. Average power is also known as active power or true power.

Also, average power can be written as

\\P_{avg}=apparent \ power\times cos\phi

Apparent power is measured in VA(Volt Ampere)

Power Factor

The power factor cosɸ can be calculated as-

cos\phi=\frac{Average \ power}{Apparent\ power}

Cosɸ can also be calculated from impedance triangle. Refer to the impedance triangle discussed above.

Reactive Power (Wattless Power)

Reactive\ Power=V_{rms}I_{rms}sin\phi

Reactive power is measured in VAr (Volt Ampere reactive)

Power Triangle

1653630747576

From the power triangle ɸ can be computed using different trigonometric ratios.

cosɸ=Active Power/Apparent Power

sinɸ=Reactive Power/Apparent Power

tanɸ=Reactive Power/ Active Power

Some Points To Remember

  • For a purely resistive circuit the instantaneous current is in phase with the instantaneous voltage. That is for VS=Vmsinωt, the current I=Imsinωt.

  • For a purely inductive circuit, the instantaneous voltage leads the current by 900. That is if VS=Vmsinωt, I=Imsin(ωt-?/2)

  • For a purely capacitive circuit, the instantaneous voltage lags the current by 900. That is if VS=Vmsinωt, IS=Imsin(ωt+?/2)

  • For a series RLC circuit if source voltage VS=Vmsinωt, IS=Imsin(ωt-ɸ) and the value of ɸ may be positive or negative depending on the value of inductive and capacitive reactance. If XL>XC, the current lags behind the voltage. If XC>XL current leads to the voltage.

Most Scoring concepts for NEET
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Question: (JEE Main 2019)

An alternating voltage V(t)=220sin100?t volt is applied to a purely resistive load of 50Ω. The time taken for the current to rise from half of the peak value to the peak value is:

Solution-

I0/2=I0sinωt

I0/2I0=sinωt

½=sinωt

ωt=?/6

Given ω=100?

100?t=?/6, therefore t=1/600 or =1..67milli seconds. This is the time to reach half the peak value from zero.

Peak value occurs at ωt=?/2. So time taken to reach peak value from zero=1/200=5milli seconds.

The time taken from half of the peak to the peak value=5-1.67=3.3milli seconds

Series Resonance

Resonance is the characteristic of the RLC series circuit. Resonance occurs when the value of capacitive and inductive reactance are equal(XC=XL). The frequency at which XC=XL is known as resonant frequency ⍵0. At ⍵0, XC-XL=0, impedance becomes minimum and current I become maximum and Imax=Vmax/R. And the value of resonant frequency is-

w_0=\frac{1}{\sqrt{LC}}

And the power factor at resonance=1

Frequency Response Or Resonant Curve

The curve represents the variation of current amplitude with respect to frequency.

1653630746608

The sharpness of resonance is measured by the quality factor Q.

Q=⍵0L/R. Also

Q=1/(⍵0RC)

As Q increases the sharpness also increases. From the frequency response, we can say that the Q factor of (i) is greater than the Q factor of (ii) as the sharpness of the first curve is more.

Suppose we choose a frequency other than ⍵0 such that the current magnitude is 1/√2 times the maximum value or power dissipated by the circuit is half of maximum value. There will be two such frequencies for which the current magnitude is 1/√2 times the maximum value, ⍵1<⍵0 and ⍵2>⍵0. The magnitude of ⍵0-⍵1=⍵2-⍵0 =?⍵. Here ⍵1 and ⍵2 are half power frequencies.

The difference ⍵2-⍵1 = 2?⍵ is known as the bandwidth and bandwidth 2?⍵= R/L. Therefore Q=⍵0L/R =⍵0/2?⍵=⍵0/(⍵2-⍵1)

1653630752934

Past 6 Years NEET Questions On RLC Series Circuit

NEET 2016

An inductor 20 mH, a capacitor 50 ?F and a resistor 40 Ω are connected in series across a source of emf V = 10 sin 340 t. The power loss in the A.C circuit-

Solution

Power loss in the circuit is asked. We have to find the average power.

Given Vm=10, ⍵=340. To find the average power we need to find Im and cosɸ

\\I_m=\frac{V_m}{Z}=\frac{10}{Z} \\cos\phi=\frac{R}{Z}\\P_{avg}=\frac{1}{2}V_mI_mcos\phi\\=V_m\times\frac{V_m}{2Z}\times\frac{R}{Z}=\frac{V_m^2R}{2Z^2}\\\\

Z=\sqrt{R^2+(\omega L-\frac{1}{\omega})^2}

=\frac{1}{2}\left [ \frac{100\times40}{1600+(340\times20\times10^{-3}-\frac{1}{340\times50\times10^{-6}})^2} \right ]\\=\frac{2000}{1600+(6.8-58.82)^2}\\=\frac{2000}{4306}=0.464W

NEET 2018

An inductor 20 mH, a capacitor 100 ?F and a resistor 50 Ω are connected in series across a source of emf V = 10 sin 314 t. The power loss in the circuit is

Solution: 0.79W

This question is similar to the NEET 2016 question and the values only differ. Try to solve it yourself.

NEET 2021

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts as shown in the figure.

1653630751867

The potential difference across L, C and R is 40 V, 10V and 40V, respectively. The amplitude of the current flowing through the LCR series circuit is 10√2 A. The impedance of the circuit is-

Solution:

Z=Vrms / Irms

\\Z=\frac{\sqrt{V_R^2+(V_L-V_C)^2}}{I_{rms}}\\=\frac{\sqrt{40^2+30^2}}{10\sqrt{2}/\sqrt{2}}=5\Omega

NEET 2020

A series of LCR circuits is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is ?/3 If instead C is removed from the circuit, the phase difference is again ?/3 between current and voltage. The power factor of the circuit is

Solution:

\begin{aligned} &\text { For only } \mathrm{RC}:\phi_{\mathrm{RC}}=\frac{\pi}{3}\\ &\tan \left(\frac{\pi}{3}\right)=\frac{\mathrm{X}_{\mathrm{c}}}{\mathrm{R}} \Rightarrow \mathrm{X}_{\mathrm{c}}=\sqrt{3} \mathrm{R}\\ &\text { For only } \mathrm{RL}:\phi_{\mathrm{RL}}=\frac{\pi}{3}\\ &\tan \left(\frac{\pi}{3}\right)=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}} \Rightarrow \mathrm{X}_{\mathrm{L}}=\sqrt{3} \mathrm{R}\\ &\text { For RLC:- }\\ &\tan (\phi)=\frac{\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}=\frac{\sqrt{3} \mathrm{R}-\sqrt{3} \mathrm{R}}{\mathrm{R}}=0 \Rightarrow \phi=0 \Rightarrow \cos \phi=1 \end{aligned}

NEET 2021

A series LCR circuit containing 5.0 H inductor 80 capacitor ?F and 40Ω resistor is connected to a 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

(1) 25 rad/s and 75 rad/s (2) 50 rad/s and 25 rad/s (3) 46 rad/s and 54 rad/s (4) 42 rad/s and 58 rad/s

Solution:

Power =Po/2 for half power frequencies. 2?⍵ the Bandwidth of resonance curve= R/L

\\w_0=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{5\times80\times 10^{-6}}}=50rad/sec.\\2\Delta w=\frac{R}{L}\\\Delta w=40/10=4rad/sec

\\w_0-w_1=4\\w_1=50-4=46rad/s

\\w_2-w_0=4\\w_2=50+4=54rad/s

So at 46 rad/s and 54 rad/s P=P0/2

So option (3) 46 rad/s and 54 rad/s is right

Practice Question

  1. A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistanceR= 3k\Omega, an inductor of inductive reactance X_{L}= 250\pi\, \Omega and an unknown capacitor. Find the value of capacitance to maximize the average power

  2. In a series LCR circuit, the inductive reactance (XL) is 10\Omegaand the capacitive reactance (XC) is 4\Omega. The resistance (R) in the circuit is 6\Omega. What is the power factor of the circuit?

  3. An AC circuit has R=100 \Omega, C= 2\mu F and L = 800 mH, connected in series. Find the quality factor of the circuit.

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Questions related to NEET

Have a question related to NEET ?

The Madhya Pradesh Medhavi Chhatra Yojana (also known as the Medhavi Yojana) provides scholarships to meritorious students based on their performance in the 12th board examinations.the percentage should be more than 75 percent for mp board students and for CBSE and icse it is 85 percent.


You can apply for scholarship and If you come into the meritorious students then the amount is even more than 25000.




If you belong to any school then they will collect your bank information So all in all you do not have to do anything, all the work is to be done by the school. You just enjoy.




Hope it helps

From your profile it is clear that you are asking about pharmacy admission through neet so,yes there are some colleges in India which considers NEET score for admission to pharmacy programs.

Other than NEET some state colleges use their own entrance exam like MHT CET, CUET, AP EAMCET, TS EAMCET, KCET, KEAM, and Graduate Pharmacy Aptitude Test (GPAT) for pharmacy.

If you are not satisfied with answer ask again i will try to help you better..

Here are top pharmacy colleges and their admission criteria you can consider

https://pharmacy.careers360.com/colleges/list-of-pharmacy-colleges-in-india

If your daughter is currently studying in a CBSE affiliated school in Qatar and has been living abroad for the past few years, she will likely qualify for an NRI seat when applying for NEET, as she meets the criteria of being an Indian citizen residing abroad and completing her 10th and 12th education from a foreign country.

NRI students can apply NEET UG under NRI category. Your daughter will be applying for seats under AIQ quota i.e 15% seats only .some states dont give reservation to NRI like Karnataka but some states like gujarat has NRI reservation.while considering colleges check specific eligibility criteria of the medical colleges you are applying to, as there may be minor variations in their NRI admission policies.

Have a look on details of NRI category NEET admission

https://medicine.careers360.com/articles/nri-quota-for-neet

Hello,

Yes, it is possible to get admission into medical-related courses without clearing the NEET exam. Here’s how:

  1. Alternative Medical Courses :

    • B.Sc. Nursing : Colleges like AIIMS (for nursing), Christian Medical College (CMC), Vellore , and St. John's Medical College, Bengaluru offer nursing programs.
    • B.Sc. Biotechnology/Biomedical Science : Jamia Millia Islamia, Delhi and Manipal Academy of Higher Education provide such programs.
  2. Allied Health Sciences :

    • Programs such as B.Sc. Radiology , B.Sc. Medical Laboratory Technology (MLT) , and B.Pharm are offered at institutions like Amity University , Lovely Professional University (LPU) , and SRM University, Chennai .
  3. Paramedical Courses :

    • Courses like Physiotherapy (BPT) , Occupational Therapy , and Optometry are available at Manipal College of Health Professions and Apollo Institute of Hospital Administration .
  4. Overseas Admissions :

    • Countries like the Philippines , Russia , and China offer MBBS without NEET but require other eligibility criteria.

These colleges and courses offer reputable options outside of the NEET pathway.

To know more, visit : https://medicine.careers360.com/articles/medical-courses-without-neet

Hope it helps !

There is no other major government examination in India that overlaps with the NEET syllabus to provide similar careers in the medical field. NEET is, however the gateway to medical and dental colleges in the country.


In case you wish to pursue other fields of science, here are your options:


1. Engineering:


JEE Main: This examination offers entry to engineering colleges, providing a vast number of courses in engineering.

2. Other Related Health Sciences:


B.Sc Nursing: Eligibility criteria differ for this course, such as Physics, Chemistry, Biology, and English

B.Pharm: This could be pursued after 12th with PCB

B.Sc Biotechnology, Microbiology, Biochemistry, etc: These are courses one takes if a person interested in the life sciences and other related studies.

Note:

Eligibility: Remember that eligibility criteria differ for courses and universities.

Entrance Exams: Prepare for entrance exams that are related to NEET, JEE Main, or whichever the university-specific tests may be.

Guidance Counseling: Participate in the process of counseling to get a seat in the preferred college and course.

If you hold an ardent passion for a career in the healthcare sector, keep researching and consider the following options like research or pharmaceutical industry or public health.

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Column I ( Salivary gland)

 

Column II ( Their location)

Parotids

I

Below tongue

Sub-maxillary / sub-mandibular

Ii

Lower jaw

Sub-linguals

Iii

Cheek

Option: 1

a(i), b(ii) , c(iii)

 


Option: 2

a(ii), b(i), c(iii)

 


Option: 3

a(i), b(iii), c(ii)


Option: 4

a(iii), b(ii), c(i)


Ethyl \; ester \xrightarrow[(excess)]{CH_{3}MgBr} P

the product 'P' will be ,

Option: 1


Option: 2


Option: 3

\left ( C_{2}H_{5} \right )_{3} - C- OH


Option: 4


 

    

           

 Valve name                            

             

Function

    I   Aortic valve     A

Prevents blood from going backward from the pulmonary artery to the right ventricle.

    II   Mitral valve     B

 Prevent blood from flowing backward from the right ventricle to the right atrium.

    III   Pulmonic valve     C

 Prevents backward flow from the aorta into the left ventricle.

    IV   Tricuspid valve     D

 Prevent backward flow from the left ventricle to the left atrium.

 

Option: 1

I – A , II – B, III – C, IV – D


Option: 2

 I – B , II – C , III – A , IV – D


Option: 3

 I – C , II – D , III – A , IV – B


Option: 4

 I – D , II – A , III – B , IV – C 

 

 


Column A Column B
A

a) Organisation of cellular contents and further cell growth.  

B

b) Leads to formation of two daughter cells.

C

c) Cell grows physically and increase volume proteins,organells.

D

d)  synthesis and replication of DNA.

Match the correct option as per the process shown in the diagram. 

 

 

 

Option: 1

1-b,2-a,3-d,4-c
 


Option: 2

1-c,2-b,3-a,4-d


Option: 3

1-a,2-d,3-c,4-b

 


Option: 4

1-c,2-d,3-a,4-b


0.014 Kg of N2 gas at 27 0C is kept in a closed vessel. How much heat is required to double the rms speed of the N2 molecules?

Option: 1

3000 cal


Option: 2

2250 cal


Option: 3

2500 cal


Option: 4

3500 cal


0.16 g of dibasic acid required 25 ml of decinormal NaOH solution for complete neutralisation. The modecular weight of the acid will be

Option: 1

32


Option: 2

64


Option: 3

128


Option: 4

256


0.5 F of electricity is passed through 500 mL of copper sulphate solution. The amount of copper (in g) which can be deposited will be:

Option: 1

31.75


Option: 2

15.8


Option: 3

47.4


Option: 4

63.5


0.5 g of an organic substance was kjeldahlised and the ammonia released was neutralised by 100 ml 0.1 M HCl. Percentage of nitrogen in the compound is

Option: 1

14


Option: 2

42


Option: 3

28


Option: 4

72


0xone is

Option: 1

\mathrm{KO}_{2}


Option: 2

\mathrm{Na}_{2} \mathrm{O}_{2}


Option: 3

\mathrm{Li}_{2} \mathrm{O}


Option: 4

\mathrm{CaO}


(1) A substance  known as "Smack"

(2) Diacetylmorphine

(3) Possessing a white color

(4) Devoid of any odor

(5) Crystal compound with a bitter taste

(6) Obtained by extracting from the latex of the poppy plant

The above statements/information are correct for:

Option: 1

Morphine


Option: 2

Heroin


Option: 3

Cocaine


Option: 4

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4 Jobs Available
Research Associate

If we talk about a career as a research associate, it all comes down to one thing - curiosity towards nature and the passion to find answers. A career as a research associate is full of thrill and excitement. However, a research associate also faces a lot of challenges and failures while working on a project. A job of a research associate includes a spectrum of Science as a subject in detail. 

2 Jobs Available
Drug Inspector

A career as a Drug Inspector is regarded as one of the most diverse in the field of healthcare and pharmacy. Candidates must undergo a screening process administered by the UPSC and or SPSCs in order to become drug inspectors. Those who manage it through the selection process will have a rewarding career with a high salary.

2 Jobs Available
Biotechnologist

A Biotechnologist is a professional who possesses strong knowledge and techniques that are utilised in creating and developing innovative products that improve the quality of human life standards. A biochemist uses biological organisms to create and improve goods and procedures for agriculture, medicine, and sustainability. He or she researches the genetic, chemical, and physical characteristics of cells, tissues, and organisms to determine how they can be used industrially.

2 Jobs Available
R&D Personnel

A career as R&D Personnel requires researching, planning, and implementing new programs and protocols into their organization and overseeing new products’ development. He or she uses his or her creative abilities to improve the existing products as per the requirements of the target market.

2 Jobs Available
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