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

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?

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

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Option c) is the right answer.

Phasor Diagram Of Series RLC Circuit

Phasor diagram for V_L>V_C

1653630753171

Phasor diagram for V_C>V_L

1653630754041

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

Resultant Voltage Of LCR Series Circuit

Question (JEE Main 2014)

When the RMS voltages V_L, V_C and V_R 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 V_L: V_C: V_R = 1:2:3. If the RMS voltage of the AC source is 100 V, then V_R (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 X_L=⍵L and X_C=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.

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 V_S=V_msinωt, the current I=I_msinωt.
For a purely inductive circuit, the instantaneous voltage leads the current by 900. That is if V_S=V_msinωt, I=I_msin(ωt-?/2)
For a purely capacitive circuit, the instantaneous voltage lags the current by 900. That is if V_S=V_msinωt, I_S=I_msin(ωt+?/2)
For a series RLC circuit if source voltage V_S=Vmsinωt, IS=I_msin(ωt-ɸ) and the value of ɸ may be positive or negative depending on the value of inductive and capacitive reactance. If X_L>X_C, the current lags behind the voltage. If X_C>X_L current leads to the voltage.

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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(X_C=X_L). The frequency at which X_C=X_L is known as resonant frequency ⍵₀. At ⍵₀, X_C-X_L=0, impedance becomes minimum and current I become maximum and I_max=V_max/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 V_m=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=V_rms / I_rms

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

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 =P_o/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

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance $R= 3k\Omega$ , an inductor of inductive reactance $X_{L}= 250\pi\, \Omega$ and an unknown capacitor. Find the value of capacitance to maximize the average power
In a series LCR circuit, the inductive reactance (XL) is 10 $\Omega$ and the capacitive reactance (XC) is 4 $\Omega$ . The resistance (R) in the circuit is 6 $\Omega$ . What is the power factor of the circuit?
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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Have a question related to NEET ?

What subjects are required for neet if the Indian origin student is doing IB board

Hello Hema,

For an Indian origin student pursuing the IB (International Baccalaureate) board , the required subjects for NEET eligibility are:

Mandatory Subjects:

Biology/Biotechnology (Higher Level or Standard Level)
Chemistry (Higher Level or Standard Level)
Physics (Higher Level or Standard Level)
English (at any level)

Key Requirements:
The student must complete these subjects at the Diploma Level (Grades 11 and 12) .
Minimum Marks:
- General category: 50% aggregate in Physics, Chemistry, and Biology (PCB).
- SC/ST/OBC: 40% aggregate in PCB.
  
  Important Notes for IB Students:
Ensure that your IB diploma is recognized by the Association of Indian Universities (AIU) as equivalent to the 10+2 system in India.
If Physics is not part of your IB subject selection, you will need to study it as an additional subject through a recognized board (such as NIOS).
You must also fulfill the age criteria, typically being at least 17 years old by December 31 of the admission year .

By meeting these requirements, IB students are eligible to apply for the NEET examination in India.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

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kumardurgesh1802 11 January,2025

I was born in May 19/ 2008 I am eligible to write neet in 2025 because candidate should 17 year old after the exam completion I am going to be 17 so I can give my neet exam in 2025

Yes ofcourse you can appear in NEET 2025 if you are born in may 2008.

According to the NEET age criteria, candidates must have completed the age of 17 years at the time of admission or will attain the same by December 31, 2025.

However,There is no upper age limit for NEET

Also,you have to fulfill other eligibility criteria for NEET

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sadafreen356 11 January,2025

neet ke question practice ki book

Hello Ayush,

Here are some recommended books for NEET question practice :

"Trueman's Objective Biology" – Great for biology practice with detailed explanations.
"Concepts of Physics by H.C. Verma" – Excellent for Physics concepts and practice problems.
"Objective Chemistry by R.K. Gupta" – Offers extensive question banks for Chemistry.
"NEET 40 Days Crash Course" by MTG – A useful guide for last-minute practice with concise questions.
"Previous Years' NEET Solved Papers" by Arihant – To practice past NEET questions for better exam preparation.
"Disha NEET Guide" – A comprehensive book with practice questions for all subjects.

These books will help you improve your speed and accuracy for the NEET exam.

For more practice I will recommend you to go with NEET PYQs. Click Here for NEET PYQs.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

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kumardurgesh1802 11 January,2025

I was born on 5may,2009, can I give neet 2026

Hello aspirant,

For students in all categories, the minimum age requirement is 17 years old as of December 31 of the year of admission. Therefore, candidates must be born on or before December 31st in order to be eligible for the reduced age limit. There is no restriction on the maximum age at which applicants may take the NEET exam.

So, yes you are eligible for NEET 2026.

Thank you

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Sajal Trivedi 10 January,2025

Which colleges offer bamd without neet

In India, NEET (National Eligibility cum Entrance Test) is mandatory for admission to Bachelor of Ayurvedic Medicine and Surgery (BAMS) in all colleges, whether government or private. Without NEET, you cannot pursue BAMS as per current regulations set by the Ministry of AYUSH.

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A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

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Veterinary Doctor

A veterinary doctor is a professional, working in animal healthcare. He or she conducts medical examinations, diagnoses, and treats various illnesses of animals. Animals have distinct internal organs and functions, requiring specialised attention from a veterinary doctor. A doctor who treats humans cannot offer the same level of care to animals due to these variations. Therefore, a veterinary doctor plays a critical role in animal welfare.

Veterinary professionals prevent illness by providing vaccines and offering advice on animal nutrition and overall health. Their knowledge extends beyond household animals and includes livestock, wildlife, and exotic animals. Individuals who love animals and want to treat their illnesses, injuries, and diseases must opt for a career as a veterinary doctor.

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Speech Therapist

Speech therapists are essential medical professionals addressing speech disorders. Whether it's delayed speech in children or difficulties in pronunciation, these experts play a crucial role. This article explores how to become a speech therapist in India, covering courses, colleges, and the responsibilities of this impactful profession.

4 Jobs Available

Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.

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Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available

Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

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Anatomist

Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.

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Narcotics Officer

A Narcotics Officer is an officer employed by the state to investigate the usage of drugs and their trafficking. A narcotics officer conducts undercover operations, investigates suspected drug dealers, executes raids and other appropriate actions for arresting these traffickers to reduce the circulation of drugs in the country.

A narcotics officer works in collaboration with other government agencies to stop drug trafficking at borders. He or she engages with various NGOs and public organisations to teach people about the dangerous effects of drug usage. A narcotics officer plays an important role in reducing the illegal activities of drug dealers and the circulation of drugs in the nation.

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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.

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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