Problem Solving 5: Ampere S Law: Fill & Download for Free

Taken from my Blog: How to become IITianPhysics was my strongest subject in JEE. I learnt it so well that after 9 years, I can still recall most of it.When I decided to teach physics, I needed just 30 minutes to read formula and main concepts in any chapter to recall everything I studied 9 years back.Just 30 minutes = full revision of a chapter after 9 years. Now I am expert in physics again.I am able to easily recall because I had very effective learning techniques; Here I will share what is the bet way to learn physics:1. Learn Concepts:"If your concepts are clear you will do great in physics."In any topic of physics you must learn:a) Basic Law: e.g. Newton's Law, Gravitation law, Ampere's Law, Bernoulli's Equation etc. These laws are foundation stone of Physics. You must know these laws in detail. You should know application & exception of these laws and how to use these laws.b) Derivation of the formula: In physics, many formulas are derived from Basic laws. You should not only remember the formula but also its derivation. Derivation with each step understood in details.c) Constraint of the formula:In derivation of formula, we assume some constraints and put a boundary to application of it. If these constrains are broken we can no longer apply the formula.Most of the time, we remember the formula but forget the constraint and apply the formula outside its applicable boundary.E.g. S = ut + (1/2)at^2. This is valid only when acceleration is constant. If acceleration is not constant, we can no longer apply this formula.Now the problem arises; How can we solve questions, where our formula is not valid?Here is the thumb rule:If constraint is broken, do not apply the formula. Take a small part (disgustingly small dx part), apply the basic law and write a differential equation. Integrate it then put limiting condition.For more details on constrains and use of integration read (Where and how to use integration?)d) Application: Learn the application of formula and basic laws.E.g. law of energy conservation can be used in friction-less projectile motion, pendulum, springs, when earth rotates around sun etc.Also learn where you cannot apply theses conceptsE.g. When friction is present you cannot use energy conservation in a significant way.e) Understand each and every step: Whenever you learn any solved problem or derivation; never mug up any step but understand every step. You must understand;What's the significance of this step?How can I apply them? How can I apply them in other problems?What principle are they based on? How do they fit in with what I already know?You must analyze each and every step of whatever you learn.When you learn anything in physics you must ensure, you learnt;Basic LawFormulaIt's derivationConstraintsHow to use integration when constraint is brokenApplication and non-application.Understand each and every stepThese all points combined are called concepts of physics.2. First learn Basics than practice to become an expert:To be an expert in physics you need to follow these three steps:Step-1: Learn basic mathematicsBasic mathematics is the foundation base of physics. If you want to do any good in physics you must have very sound foundation of basic mathematics. This will include following topics:Dimensions: Have a keen eye for dimensions. I will rate it most important mathematical skill, even more important than integration.Number System: surds & exponential, Multiplication table (This will help you to overcome silly mistakes.)Basic arithmetic: Solve equations; work with unknown quantities, degree of freedom.Logarithm: Graph of log(x), Change base, use of logarithm in integrationTrigonometry: Sin, Cos relation, basic trigonometric equations, relation between parallel lines and angles (useful in free body diagrams.)Vectors: Components of vector, modulus, multiplication of vectors, addition and subtraction of vectors.Co-ordinate geometry: Lines, angles and slope.Integration and differentiation: Definition, basic integration/ diffrentiation and Where and how to use integration?These topics are easy to learn. Basic knowledge of these topics is enough but you must be very conversant with it. Practice is necessary to sharpen this sward.If you are not conversant with these topics; you will commit more silly mistakes. Many students have problem with this basic skill but they do not realize it.See the check list below, If you any have problem listed you should revisit and learn basic mathematics.Silly mistake in very simple calculation. e.g. 3*15 + 5 = 45. Revisit number system, remember table upto 20 and never try to do calculation faster.Has a problem to find angle in free body diagram or often you use wrong angles. Revisit trigonometry and vectors.Take wrong component of force. Revisit trigonometry, vectors and co-ordinate geometry.Difficulty in solving equation. Revisit basic arithmeticStep-2: Learn basic Physics: Follow point 1.Step-3: Amalgamation: An attempt to solve unsolved problemsIn step 1 & 2 you have learnt basic, now in this step you will become expert in Physics. We will work on complex, tough and unsolved problems.A complex problem is nothing but the combination of several easy problems. Most students will solve these easy problems separately but to solve a complex problem they need to think systematically, identify these easy problems and recall many concepts at the same time .This systematical thinking, identification and power to recall make these problems difficult but these qualities can be developed with a well guided approach.Good news, I am here to guide you. Now sit tight and be ready for a flight.Systematical thinking and Identification of problems:Practice is the key to develop these skills. More practice means more control over basics means easy amalgamation of different concepts.Approach difficult problems with positive attitude. You can solve any problem, It does not matter how much time you will need and it is OK to refer some notes/ books. This is your learning phase not the exam.Use a trace back method to solve these problems. First identify what is being asked and recall concepts related to it.I will give an example:E.g. ‘A particle is projected with a speed u at an angle ѳ with the horizontal. Consider a small part of it’s path at height h and take it approximately to be a circular arc. What is the radius of curvature at this point?'We need to find 'radius of curvature'. This is related to circular motion so recall concepts related to circular motion, recall every thing related to circular motion than we will choose what we can use. Concepts:v = wr,r = ѳ * arc length,A centrifugal force is necessary to maintain circular motion. This force is perpendicular to direction of velocity.Now refer to data given in question and choose the concept we can use.We cannot use v = wr or r = ѳ * arc length, as w & ѳ are not knownOnly force acting on particle is mg (gravitation force), so centrifugal force is provided by gravity. This concept can be used.Now recall the concepts related to the problem, We will use them together.Many different concepts are involved. Circular motion, projectile motion, gravitation, newtons law.Concepts of circular motion will give us a radial acceleration (v*v/r) and its direction perpendicular to velocity.Concepts of gravity will give us a force mg acting downwards.Concepts of newton's law will help us to balance force & acceleration equation (F = ma) along the line perpendicular to velocity.Concept of projectile will give us velocity at height h and angle between horizontal and velocity.Now I leave this solution for readers. If you do not understand any part feel free to sent me a message. Mayank Jain3. Importance of self-studyTo become expert in anything, You must learn it and practice it. I have seen many students who rush through learning part and move to practice but without proper learning practice will be ineffective. I am not telling you practice is not important but learning is more important.Just answer these questions.How many times you have revised your class notes?How many times you have referred a book to learn a concept?How many times you have imagined how, where and when we use a concept? How many times you have taken notes?How many times you have practiced a problem?If answer to last question outnumbers all other question then you need to redefine learning strategy. At the initial phases of the preparation learning should take at-least 25% of home study time.Follow these simple steps to improve alot:Always revise your class notes after the classLearn from at-least one other source what you have learnt in classTake notes for future revisionAt the end of week; revise at-least once what you learntAt end of the month go through all you have learnt till now.Last point may seem impossible but believe me, it is possible. I have done it, It all depend on how skilled you are on taking notes. I will write blog on note taking skills so follow my book for updates. How to become an IITian.4. Recommended Material/ booksRead more at Recommended Study Material for IIT JEEFollow my blog for more such post How to become an IITianYou can find content of the book at Content: Quora Book"Happy Learning"

These type of problems can be solved in many-many ways. One way is below:Follow Kirchhoff ’s Current &Voltage Law along with Ohms Law.Break the circuit first i.e.Putting it this way will make it easy, illustration wise. Start calculating series and parallel registers now. J1 and J2 are your two Junctions.Resisters R2, R3, R4 are in series. Therefore their total Resistance is 20Ω. Now consider this 20Ω register as R7. This R7 is parallel with R6.Using reciprocal of reciprocal (formula):We get the value of both parallel resistors (R7 & R6) as 8.57Ω. We will name it as R8. So now we have:Total resistance (load) of the circuit is 5+8.57+5 = 18.57Ω (resistors in series will addup)Total Voltage = 15 VTotal Resistance = 18.57 Ω.Therefore (Ohm’s Law) I (current) = V / R = 15 / 18.57 = 0.81 Amperes.If you notice, we have three segments here. One is from 15v supply to J1 (illustration wise), second is from J1 to J2 and third is from J2 to Grnd. Using current above, calculate the voltages for these three segments. This would beTo check, add the three voltages i.e. 4.05 + 6.94 + 4.05 = 15 volts (rounded)Now we will build back the circuit, in the reverse order.The individual segments’ currents are calculated using Ohm’s law.For R7 I = V / R = 6.94 / 20 = 0.347A and R6 is 0.462AWe will concentrate on the segment J1 - J2.According to Kirchoff’s Current & Voltage law - putting it simply - in Parallel circuits, the currents divide and in Series circuits the voltage divide. Therefore we have used 6.94 v (the voltage of that segment) to calculate the divided current between R7 and R6 parallel resistors.Building up or breaking up R7 / 20Ω resistor again we get our three resistors R2, R3, R4 back.Now voltage for segment J1-J2 is 6.94 v. and the current flowing through R2, R3 and R4 resistors is 0.347A only (as calculated above). Now we have to calculate the individual voltages of the resistors in series i.e. R2, R3, R4. Accordingly, V=IR and…Voltage for R2 = 0.347A x 5Ω = 1.735vVoltage for R3 = 0.347A x 10Ω = 3.47 v andVoltage for R4 = 0.347 x 5 Ω = 1.735 vAdding the three voltages we will get 1.735+3.47+1.735 = 6.94 volts (the total segment voltage)and Now we haveTotal current of three segments will remain 0.81 amps (segment J1-J2 0.347 + 0.462 = 0.81 amps.

Physics is my strongest subject .Just 30 minutes = full revision of a chapters . Now I am expert in physicsI have very effective learning techniques; Here I will share what is the bet way to learn physics:1. Learn Concepts:"If your concepts are clear you will do great in physics."In any topic of physics you must learn:a) Basic Law: e.g. Newton's Law, Gravitation law, Ampere's Law, Bernoulli's Equation etc. These laws are foundation stone of Physics. You must know these laws in detail. You should know application & exception of these laws and how to use these laws.b) Derivation of the formula: In physics, many formulas are derived from Basic laws. You should not only remember the formula but also its derivation. Derivation with each step understood in details.c) Constraint of the formula:In derivation of formula, we assume some constraints and put a boundary to application of it. If these constrains are broken we can no longer apply the formula.Most of the time, we remember the formula but forget the constraint and apply the formula outside its applicable boundary.E.g. S = ut + (1/2)at^2. This is valid only when acceleration is constant. If acceleration is not constant, we can no longer apply this formula.Now the problem arises; How can we solve questions, where our formula is not valid?Here is the thumb rule:If constraint is broken, do not apply the formula. Take a small part (disgustingly small dx part), apply the basic law and write a differential equation. Integrate it then put limiting condition.For more details on constrains and use of integration read (Where and how to use integration?)d) Application: Learn the application of formula and basic laws.E.g. law of energy conservation can be used in friction-less projectile motion, pendulum, springs, when earth rotates around sun etc.Also learn where you cannot apply theses conceptsE.g. When friction is present you cannot use energy conservation in a significant way.e) Understand each and every step: Whenever you learn any solved problem or derivation; never mug up any step but understand every step. You must understand;What's the significance of this step?How can I apply them? How can I apply them in other problems?What principle are they based on? How do they fit in with what I already know?You must analyze each and every step of whatever you learn.When you learn anything in physics you must ensure, you learnt;Basic LawFormulaIt's derivationConstraintsHow to use integration when constraint is brokenApplication and non-application.Understand each and every stepThese all points combined are called concepts of physics.2. First learn Basics than practice to become an expert:To be an expert in physics you need to follow these three steps:Step-1: Learn basic mathematicsBasic mathematics is the foundation base of physics. If you want to do any good in physics you must have very sound foundation of basic mathematics. This will include following topics:Dimensions: Have a keen eye for dimensions. I will rate it most important mathematical skill, even more important than integration.Number System: surds & exponential, Multiplication table (This will help you to overcome silly mistakes.)Basic arithmetic: Solve equations; work with unknown quantities, degree of freedom.Logarithm: Graph of log(x), Change base, use of logarithm in integrationTrigonometry: Sin, Cos relation, basic trigonometric equations, relation between parallel lines and angles (useful in free body diagrams.)Vectors: Components of vector, modulus, multiplication of vectors, addition and subtraction of vectors.Co-ordinate geometry: Lines, angles and slope.Integration and differentiation: Definition, basic integration/ diffrentiation and Where and how to use integration?These topics are easy to learn. Basic knowledge of these topics is enough but you must be very conversant with it. Practice is necessary to sharpen this sward.If you are not conversant with these topics; you will commit more silly mistakes. Many students have problem with this basic skill but they do not realize it.See the check list below, If you any have problem listed you should revisit and learn basic mathematics.Silly mistake in very simple calculation. e.g. 3*15 + 5 = 45. Revisit number system, remember table upto 20 and never try to do calculation faster.Has a problem to find angle in free body diagram or often you use wrong angles. Revisit trigonometry and vectors.Take wrong component of force. Revisit trigonometry, vectors and co-ordinate geometry.Difficulty in solving equation. Revisit basic arithmeticStep-2: Learn basic Physics: Follow point 1.Step-3: Amalgamation: An attempt to solve unsolved problemsIn step 1 & 2 you have learnt basic, now in this step you will become expert in Physics. We will work on complex, tough and unsolved problems.A complex problem is nothing but the combination of several easy problems. Most students will solve these easy problems separately but to solve a complex problem they need to think systematically, identify these easy problems and recall many concepts at the same time .This systematical thinking, identification and power to recall make these problems difficult but these qualities can be developed with a well guided approach.Good news, I am here to guide you. Now sit tight and be ready for a flight.Systematical thinking and Identification of problems:Practice is the key to develop these skills. More practice means more control over basics means easy amalgamation of different concepts.Approach difficult problems with positive attitude. You can solve any problem, It does not matter how much time you will need and it is OK to refer some notes/ books. This is your learning phase not the exam.Use a trace back method to solve these problems. First identify what is being asked and recall concepts related to it.I will give an example:E.g. ‘A particle is projected with a speed u at an angle ѳ with the horizontal. Consider a small part of it’s path at height h and take it approximately to be a circular arc. What is the radius of curvature at this point?'We need to find 'radius of curvature'. This is related to circular motion so recall concepts related to circular motion, recall every thing related to circular motion than we will choose what we can use. Concepts:v = wr,r = ѳ * arc length,A centrifugal force is necessary to maintain circular motion. This force is perpendicular to direction of velocity.Now refer to data given in question and choose the concept we can use.We cannot use v = wr or r = ѳ * arc length, as w & ѳ are not knownOnly force acting on particle is mg (gravitation force), so centrifugal force is provided by gravity. This concept can be used.Now recall the concepts related to the problem, We will use them together.Many different concepts are involved. Circular motion, projectile motion, gravitation, newtons law.Concepts of circular motion will give us a radial acceleration (v*v/r) and its direction perpendicular to velocity.Concepts of gravity will give us a force mg acting downwards.Concepts of newton's law will help us to balance force & acceleration equation (F = ma) along the line perpendicular to velocity.Concept of projectile will give us velocity at height h and angle between horizontal and velocity3. Importance of self-studyTo become expert in anything, You must learn it and practice it. I have seen many students who rush through learning part and move to practice but without proper learning practice will be ineffective. I am not telling you practice is not important but learning is more important.Just answer these questions.How many times you have revised your class notes?How many times you have referred a book to learn a concept?How many times you have imagined how, where and when we use a concept? How many times you have taken notes?How many times you have practiced a problem?If answer to last question outnumbers all other question then you need to redefine learning strategy. At the initial phases of the preparation learning should take at-least 25% of home study time.Follow these simple steps to improve alot:Always revise your class notes after the classLearn from at-least one other source what you have learnt in classTake notes for future revisionAt the end of week; revise at-least once what you learntAt end of the month go through all you have learnt till now.4. Recommended Material/ booksRead more at Recommended Study Material for IIT JEE