 Rahul Kumar

student | Physics Chemistry Maths Applied mathematics

Description

I am physics teacher having 12 years of exp.

TOTAL PROBABILITY THEOREM

TOTAL PROBABILITY THEOREM

Let E1, E2, ..., En be n mutually exclusive and exhaustive events and event A is such that it can occur with any of the events E1, E2, E3, ....... En then the probability of the occurrence of event A can be   Example:

Solution :  CONDITIONAL PROBABILITY

CONDITIONAL PROBABILITY

If A and B are two events, then the conditional probability of event A given that event B has already occured  Similarly, the probability of B given that A has already occured will be Therefore, Example:

If a pair of dice is thrown and it is known that sum of the numbers is even, then find the probability that the sum is less than 6.

Let A be the given event and let B be the event, whose probability is to be found. Then

Required probability  Physics - What is Ohm's Law?

Ohm's Law

At constant temperature, the current passing through a conductor is proportional to the potential difference between its ends. If the potential difference between the ends of a Conductor AB is V and the current through it is i, then according to Ohm's Law, where R is a constant known as Electrical Resistance of the Conductor.

Limitations of Ohm's Law

Ohm's law is applicable to metal conductors when physical constants dimensions and temperature are constant.

The Conductors that obey ohm's law are called ohmic registors.

E.g Metals

Physics - Law of Conservation of Energy - With Example

Law of Conservation of Energy

Statement :

Energy can neither be created nor destroyed but one form of energy can be transformed in to another form of energy without any loss or gain of energy.

The total energy that exists in the universe in all form remain constant.

Example :

In a battery chemical energy is converte to electrical energy.

In a dynamo, mechanical energy is converted in to electrical energy.

Verification of law of conservation of energy in case of a freely falling body:

Consider a body of mass 'm' released from Point 'A' above the surface of the earth at height 'h'.

As the body falls freely under gravity , its P.E decreases . At A :  At B we know   At point 'c'   T.E is same at point A, B, C = mgh

Physics - What is Kirchhoff's Laws

Kirchhoff's Laws

First Law :

The algebric sum of the currrents meeting at any point in a network is zero.

Explanation :

Let the currrent are meeting at junction are passing away from the junction

from Kirchhoff's first law,   This law is also called LAW OF JUNCTIONS

Second Law :

In any closed circuit the algebric sum of potential difference is ZERO.

Explanation :

Consider a network (closed) shown in a figure This is also called LOOP THEOREM

Physics : Newton's Laws of Rectilinear Motion : First Law : (Relation of force and Motion)

Newton's Laws of Rectilinear Motion : First Law : (Relation of force and Motion)

A law govering the relationship between forces and motion was completly described by Sir Issac Newton on the basis of inertia law of Galileo which asserted that if there are no external actions on a body it neither moves with a constant velocity or is at rest.Newton formulated the law as fallow :

" A body will remain in its state of rest of uniform rectilinear motion (having zero acceleration) unless it is compelled to change its state by application external force "'

OR

If the (Vector) sum of all thee forces acting on a given particle is zero then and only then the particle remains unaccelarated (i.e remains at rest or moves with constant velocity)

If the sum of all forces on a given particle is F and its acceleration is a, the above statement many also be written as Thus, if the sum of the forces acting on a particle is known to be zero, we can be sure that the particle is unaccelerated , or if we know that a particle is unaccelerated, we can be sure that the sum of forces acting on the particle is zero.

If no external forces acts on a system, the state of system does not change. Here,

State  -----> Centre of Mass

If system consist of more the one particle then newton's law is collectivly applied to centre of Mass.

Physics - What is Joule's Law

What is Joule's Law

Accorrding to Joule's law, the current passing thrrough a resistor produces heat. The quantity of heat produce 'Q' is equal to the work done by the electric field on the free electrons. If the potential differrence between the ends of resistor is 'V' and current 'i' passes through it for 't' sec. The workdone (w) in time 't' is.  This is equal to the heat produced in the resistor due to collision of free electorn with the lattice under the electric field 1. The heat produced in a given resistor in a given time is propotional to the square of the currrent. 2. The heat produced in a given resistor in a given time is propotional to the time for which the currrent exists in it and 3. The heat produced in a given resistor by a given currrent in a given time is proportional to its resistance Electric heater, electric iron, electric bulb etc are some of the instrument which work on Joule's Law and covert electrical energy to heat energy.

Electrostatics, Topic: - (Electric Field Due To Charged Sheet)

Electrostatics, Topic: - (Electric Field Due To Charged Sheet)

Work,Power & Energy, Topic: - (Potential Energy In Spring)

Work,Power & Energy, Topic: - (Potential Energy In Spring)

SETS - SOME IMPORTANT NUMBER SETS

SETS - SOME IMPORTANT NUMBER SETS

SET

A set is a collection of well defined objects which are distinct from each other

Set are generally denoted by capital letters A, B, C, .... etc. and the elements of the set by a, b, c .... etc.
If a is an element of a set A, then we write and say a belongs to A.
If a does not belong to A then we write e.g. The collection of first five prime natural numbers is a set containing the elements 2, 3, 5, 7, 11.

SOME IMPORTANT NUMBER SETS :

N = Set of all natural numbers = {1, 2, 3, 4, ....}

W = Set of all whole numbers = {0, 1, 2, 3, ....}

Z or I set of all integers    = {.... –3, –2, –1, 0, 1, 2, 3, ....}

Z+  =  Set of all +ve integers = {1, 2, 3, ....} = N.
Z–  =  Set of all –ve integers = (–1, –2, –3, ....}
Z0 =   The set of all non-zero integers. = {±1, ±2, ±3, ....}
Q =    The set of all rational numbers R = the set of all real numbers.

R–Q = The set of all irrational numbers

e.g METHODS TO WRITE A SET :

(i) Roster Method : In this method a set is described by listing elements, separated by commas and enclose then by curly brackets
e.g. The set of vowels of English Alphabet may be described as {a, e, i, o, u}

(ii) Set Builder Form : In this case we write down a property or rule p Which gives us all the element
of the set     TYPES OF SETS

Null set of Empty set :

A set having no element in it is called an Empty set or a null set or void set it is denoted by  A set consisting of at least one element is called a non - empty set or non - void set.

Example :

The set  Solution :  There is no value of x which satisfies both the above equations

Thus Singleton :

A set consisting of a single element is called a singleton set. e.g. Then set {0}, is a singleton set.

Finite Set :

A set which has only finite number of elements is called a finite set. e.g. A = {a, b, c}

Order of a finite set :

The number of elements in a finite set is called the order of the set A and is denoted O(A) or n(A). It is also called cardinal number of the set.

e.g.A={a,b,c,d}  i.e n(A)=4

Infinite set :

A set which has an infinite number of elements is called an infinite set.

e.g. A = {1, 2, 3, 4, ....} is an infinite set

Equal sets :

Two sets A and B are said to be equal if every element of A is a member of B, and every element of B is a member of A.

If sets A and B are equal. We write A = B and A and B are not equal then A != B

e.g.A={1,2,6,7} and B={6,1,2,7} i.e A=B

Equivalent sets :

Two finite sets A and B are equivalent if their number of elements are same ie. n(A) = n(B)

e.g.A={1,3,5,7}, B={a,b,c,d}

n(A) = 4 and n(B) = 4 i.e n(A) = n(B)

Note : Equal set always equivalent but equivalent sets may not be equal
Subsets :

Let A and B be two sets if every element of A is an element B, then A is called a subset of B if A is a subset of B. we write Example : A={1,2,3,4}andB={1,2,3,4,5,6,7}

i.e Proper subset :

If A is a subset of B and A != B then A is a proper subset of B. and we write

Note-1 : Every set is a subset of itself i.e. A A for all A
Note-2 : Empty set is a subset of every set

Note-3 : The total number of subsets of a finite set containing n elements is 2n

Universal set : A set consisting of all possible elements which occur in the discussion is called a Universal set and is denoted by U

Note : All sets are contained in the universal set

e.g. If A = {1, 2, 3}, B = {2, 4, 5, 6}, C = {1, 3, 5, 7} then U = {1, 2, 3, 4, 5, 6, 7} can be taken as the Universal set.
Power set : Let A be any set. The set of all subsets of A is called power set of A and is denoted by P(A)

Power set : Let A be any set. The set of all subsets of A is called power set of A and is denoted by P(A)

Let A = {1, 2}. then   then Note-1 : If then P(A) has one element

Note-2 : Power set of a given set is always non empty

Example :

Two finite sets of have m and n elements respectively the total number of elements in power set of first set is
56 more thatn the total number of elements in power set of the second set find the value of m and n
respectively.

Solution :

Number of elements in power set of 1st set = Number of elements in power set of 2nd set = Given,    Work,Power & Energy, Topic: - (Potential Energy)

Work,Power & Energy, Topic: - (Potential Energy)

Physics Cheat Sheet - Kinematics

Kinematics

Displacement

if + it's AWAY

If - it's TOWARD

Velocity (m /s )

Use Only when SPEED is CONSTANT

1. Does not include acceleration

2. Does not include starting and stoping in the same place Acceleration (m / s)

Speeding up or slowing down Kinematic Formulas

x - Direction                                                                   Y - Direction    