An complete solution for Physics



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Basic Topics in Physics

Electric Current

Current is the flow of charged particles    through a conducting medium, such as a metal wire. In other words, electric current is a measure of the amount of electrical charge transferred per unit time across any cross-section.

If dq be the charge flowing through a given cross-section in time dt, then electric current ‘I’ through the same cross-section

The S.I. unit of electric current is ampere having symbol A. The electric current through any cross-section is 1 ampere if 1 coulomb charge flows across it in 1 second.

Thus,      ampere= coulomb per second

A = Cs-1

The direction of electric current is taken as the direction of flow of positive charge. It means the direction of electric current is opposite to the direction of electrons.

On the basis of variation of its direction, the two main types of current are:

Direct Current in which the flow electric current is only in one direction and Alternating current whose magnitude changes with time and reverses its direction periodically.

Electric current is a scalar quantity. Although electric current possesses both magnitude and direction, yet it is not a vector quantity because it does not obey the rules of vector addition. Thus, the arrow heads used to indicate the direction of current in electric circuit is simply indicate the direction of flow of positive charge. Electric currents add and multiply like scalar quantity.

Current Density

Current density as word itself suggests is the density of current. It is an another way to describe the flow of charge.  The electric current density at a point in the conductor is defined as the electric current per unit area around the given point and in a direction perpendicular to the area. It may be noted that it is the characteristic property of point inside the conductor nor the conductor as a whole.In SI units, the electric current density is measured in amperes per square metre.


 Current density is important to design the electrical and electronic systems. Circuit performance depends strongly upon the designed current level and the current density then is determined by the dimensions of the conducting elements.

 For example, as integrated circuits are reduced in size, despite the lower current demanded by smaller devices, there is trend toward higher current densities to achieve higher device number in ever smaller chip areas.

High current densities have undesirable consequences. Most electrical conductors have finite, positive resistance, making the dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up.                                                                                                              

Ohm’s  Law

It states that when physical conditions remaining the same, the electric current through a conductor is directly proportional to the potential difference across its ends.

Mathematically, if V be the potential   difference and I be the current, then

    V = IR

 Where, R is a constant for the conductor and is called resistance.

Unit of Resistance

The unit of resistance is called ohm (symbol ).

If,        V =one volt and I = one ampere,

Then   R = one ohm

Thus:  volt = (ampere) (ohm)

Ohm’s Law as a Predictor of Current

As an equation, this serves as an algebraic recipe for calculating the current if potential difference and the resistance are known. This equation indicates the two variables that would  affect the amount of current in circuit.    The current in a circuit at constant temperature is directly proportional to the electric potential difference impressed across its ends and inversely proportional to the total resistance offered by the external circuit. It means when voltage of the battery is increased, current through the circuit also increases and when resistance is increased, the current decreases.

.Failure of Ohm’s law Ohm’s law is applicable for some conductors called Ohmic Conductors which have a linear dependency of potential difference on current flowing through the conductor means V proportional to I. But there are many other conductors which do not follow Ohm’s law and called Non-Ohmic Conductors like Transistors, Diodes, etc.

 The graph between V and I is expected to be a straight line which is not obtained for higher values of current. Moreover, sometimes  the relation of V and I becomes dependent on sign of V for forward and reverse bias respectivel The graph shows that when the voltage of external source is gradually increased, the current flowing through the circuit doesn’t increase up to a larger value of external voltage. But at a certain voltage (Knee voltage), the current increases abruptly. Thus current is not directly proportional to the applied voltage in some cases and in that cases Ohm’s law does not hold true.

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Physics numerical problems

NCERT BOOKS OF 10+1 & 10+2

IIT JEE Physics Preparation Books


Serial Number Name Author Type of Book Description
1Concepts of PhysicsH.C. VermaText-book for BasicsBest for Mechanics, Electrostatics, Optics, Modern Physics, Heat and waves. The book contains high quality solved numerical problems which would be of a great help in understanding the method of solving problems.
2NCERT Physics Text-book for BasicsClass XI and Class XII books for CBSE
3Problems in General PhysicsI.E. IrodovProblems and solutionsConsists of high level problems. Best for Mechanics, Electricity and Mechanism, modern Physics
4Fundamentals of PhysicsResnick, Halliday, WalkerReference BookGood for Mechanics, Electricity and Magnetism, Heat.
5Arihant PhysicsD. C. PandeyReference BookConsists of many solved problems. However must be used for reference only after understanding the basics properly
6University PhysicsSears and ZemanskyReference BookGood numerical problems
7Elements of DynamicsS.L.LoneyReference Book 
8Advanced level PhysicsNelson and ParkerReference Book 

IIT JEE Chemistry Preparation Books

Serial Number Name Author Type Description
1NCERT Chemistry Text Book for BasicsClass XI and class XII books for CBSE
2Organic ChemistryMorrison & BoydReference bookBest for strengthening conceptual knowledge
3Reaction mechanism in Organic ChemistryParmar and ChawlaReference Book 
4Arihant Chemistry Reference BookGood for preparation when there is a lot of time in hand. Not recommended if there is time constraint.
5Organic ChemistryFrancis Carey (TMH)Reference Book 
6Concise Inorganic ChemistryJ.D. LeeReference Book 
7IIT ChemistryO.P. AgarwalReference BookHighly recommended
8Numerical ChemistryR. C. MukerjeeReference Book 
9Physical ChemistryP.W.AtkinsReference Book 
10Numerical ChemistryP.BahadurReference BookSolved numerical problems are good. Chemical and Ionic Equilibrium have been explained well.
11General ChemistryEbbingReference Book 

IIT JEE Maths Preparation Books

Serial Number Name Author Type Description
1MathematicsR.S. AgarwalText Book for BasicsX and XII
2NCERT Maths Text Book for BasicsCBSE prescribed books for XI and XII
3High school mathematicsHall and KnightReference Book 
4New Pattern Mathematics fot IIT JEEM.L. KhannaReference Book 
5Algebra made easyK.P.BasuReference Book 
6A problem book in Mathematical analysisG.N. BermanReference Book 
7Calculus and analytic geometryThomas and FinneyReference Book 
8Coordinate geometryS. L. LoneyReference BookHighly recommended book by coaching centres
9Problems in calculus of one variableI.A. MaronReference BookConsidered very good for Differential Calculus
10TMH Course in Mathematics for IIT JEETata McGraw Hill PublicationsReference Book 
11Plane TrigonometryS.L. LoneyReference BookThe book contains detailed conceptual knowledge of the subject. Great for strengthening the basics of Trigonometry. Great for understanding Vectors
12Higher AlgebraBernard and ChildReference BookA high level book. Must be referred after an advanced understanding of the subject.
13Arihant Mathematics Reference Books