Physics Complete

PN Junction Diode in Forward Bias and Reverse Bias

Solving Problems on the Concept of P N Junction Diode

Dimensional Formula List One

In the previous posts we had discussed about units and dimensions concepts like the basic definitions, rules for writing units and dimensions and uses and limitations of dimensional formula.Here we are going to see the list of physical quantities, their formula,dimensional formula, CGS unit and SI unit .

Please click on the image if it is not visible clearly.

PN Junction Diode in Forward Bias and Reverse Bias

Solving Problems on the Concept of P N Junction Diode

Dimensional Formula Uses and Limitations

Dimensional Formula is the representation of fundamental quantities in a physical quantity.It gives us an idea about how the derived physical quantity is depending on fundamental quantity.For basic definitions you can go through this lesson where the present one deals with advanced concepts.

Dimensional Formula is useful for the following applications.

1.To check the correctness of the given equation. This use is based on the principle of homogeneity.

Principle of homogeneity:

It states only quantities of same dimensions can be added subtracted and equated. Hence in a Physical equation every term should have same dimensions.

2 . To convert one system of units into another system.

Eg: The numerical value of 10 joule in a new system of units in which the unit of mass is 10gm, unit of length 10cm. and unit of time 10sec. can be determined using the concept that

n₁u1 = n₂u₂

where n₁,n_{2 are the numerical values of a physical quantity and}u1,u_{2 are the different units for same physical quantity.It means the original value of physical quantity remains same even when it is represented in different system of units.}

3 . To derive the equations showing the relation between different physical quantities.

Eg: When a spherical body falls through a viscous medium the upward viscous force acting on it depends upon

1. radius r of the body

2. coefficient of viscosity of the medium and

3. velocity v of the body.

_{^{We can calculate the powers of them that how do they depend on this physical quantities using the dimensional analysis as shown below.}}

LIMITATIONS OF DIMENSIONAL SYSTEM:

1 . Dimensionless quantities cannot be determined by this method. Constant of proportionality cannot be determined by this method. They can be found either by experiment (or) by theory.

2 . This method is not applicable to trigonometric, logarthmic and exponential functions.

3.In the case of physical quantities which are dependent upon more than three physical quantities, this method will be difficult.

4 . In some cases, the constant of proportionality also posseses dimensions. In such cases we cannot use this system.

5 . If one side of equation contains addition or subtraction of physical quantities, we can not use this method.
_{^{The previous post of this site deals with velocity and acceleration concept of kinematics.}}

PN Junction Diode in Forward Bias and Reverse Bias

Solving Problems on the Concept of P N Junction Diode

Kinematics Accelaration

The previous post about kinematics deals with SPEED AND VELOCITY and it can be browsed here.

Acceleration as the rate of change of velocity with time.

The average acceleration `a over a time interval is defined as the change of velocity divided by the time interval :

`a = D v /Dt .

where v2 and v1 are the instantaneous velocities or simply velocities at time t2 and t1. It is the average change of velocity per unit time. The SI unit of acceleration is m s–2 .

On a plot of velocity versus time, the average acceleration is the slope of the straight line connecting the points corresponding to (v2, t2) and (v1, t1). The average acceleration for velocity-time graph shown in figure for different time intervals 0 s - 10 s, 10 s – 18 s, and 18 s and – 20 s are :

0 s - 10 s `a = 24 - 0 /10 - 0 = 2.4 m s–2 .

10 s - 18 s `a = 24 - 24 / 18 - 10 = 0 m s–2 .

18 s - 20 s `a = 0 - 24 / 20 - 18 = -12 m s–2.

Instantaneous acceleration is defined as rate of change of velocity at any particular instant.It is shown as a = dv/dt .The acceleration at an instant is the slope of the tangent to the v–t curve at that instant.

Since velocity is a quantity having both magnitude and direction, a change in velocity may involve either or both of these factors. Acceleration, therefore, may result from a change in speed (magnitude), a change in direction or changes in both. Like velocity, acceleration can also be positive, negative or zero.

Position-time graphs for motion with positive, negative and zero acceleration are shown in figures (a), (b) and (c), respectively.

The graph curves upward for positive acceleration; downward for negative acceleration and it is a straight line for zero acceleration.

The area under the curve represents the displacement over a given time interval.of velocity-time graph for any moving object .

Let us check for a simple case as follows.

Let an object moving with constant velocity u. Its velocity-time graph is as shown in figure.

The v-t curve is a straight line parallel to the time axis and the area under it between t = 0 and t = T is the area of the rectangle of height u and base T. Therefore, area = u × T = uT which is the displacement in this time interval.

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RELATED POSTS

One dimensional motion
Speed and Velocity

PN Junction Diode in Forward Bias and Reverse Bias

Solving Problems on the Concept of P N Junction Diode

Kinematics Velocity and Speed

The previous post in kinematics deals with one dimensional motion concept and you can browse it here.
AVERAGE VELOCITY AND AVERAGE SPEED :

Average velocity is defined as the change in position or displacement (Δx) divided by the time intervals (Δt),

v = X_{2 -}X1/t_{2 -}t1

where x2 and x1 are the positions of the object at time t2and t1, respectively. Here bar over the symbol for velocity is a standard notation used to indicate an average quantity. The SI unit for velocity is m/s or , although km/h is used in many everyday applications.

The average velocity can be positive or negative depending upon the sign of the displacement. It is zero if the displacement is zero. The following fugures shows the x-t graphs for an object, moving with positive velocity (Fig. a), moving with negative velocity (Fig. b) and at rest (Fig. c).

Average speed is defined as the total path length travelled divided by the total time interval during which the motion has taken place :

Average speed = Total path length/Total time interval

Average speed has obviously the same unit(m/s) as that of velocity. But it does not tell us in what direction an object is moving. Thus, it is always positive (in contrast to the average velocity which can be positive or negative). If the motion of an object is along a straight line and in the same direction, the magnitude of displacement is equal to the total path length.In that case, the magnitude of average velocity is equal to the average speed.

INSTANTANEOUS VELOCITY AND SPEED :The velocity at an instant is defined as the limit of the average velocity as the time interval Δt becomes infinitesimally small.

v = dx/dt
For uniformmotion, velocity is the same as the average velocity at all instants.

Instantaneous speed or simply speed is the magnitude of velocity.

One Diemensional Motion concepts part one

Motion is change in position of an object with time.Study of motion of objects along a straight line is known as rectilinear motion.

FRAME OF REFERENCE:

we need to use a reference point and a set of axes. It is convenient to choose a rectangular coordinate system consisting of three mutually perpendicular axes, labeled X-, Y-, and Z- axes.

The point of intersection of these three axes is called origin (O) and serves as the reference point. The coordinates (x, y. z) of an object describe the position of the object with respect to this coordinate system.

To measure time, we position a clock in this system. This coordinate system along with a clock constitutes a frame of reference.

Description of an event depends on the frame of reference chosen for the description. For example, when you say that a car is moving on a road, you are describing the car with respect to a frame of reference attached to you or to the ground. But with respect to a frame of reference attached with a person sitting in the car, the car is at rest.

To describe motion along a straight line, we can choose an axis, say X-axis, so that it coincides with the path of the object.

Displacement has both magnitude and direction. Such quantities are represented by vectors.

If one or more coordinates of an object change with time, we say that the object is in motion. Otherwise, the object is said to be at rest with respect to this frame of reference.

The choice of a set of axes in a frame of reference depends upon the situation. For example, for describing motion in one dimension, we need only one axis. To describe motion in two/three dimensions, we need a set of two/ three axes.

The magnitude of displacement may or may not be equal to the path length traversed by an object.

The magnitude of the displacement for a course of motion may be zero but the corresponding path length is not zero. For example, if the car starts from O, goes to P and then returns to O, the final position coincides with the initial position and the displacement is zero. However, the path length of this journey is OP + PO.

Motion of an object can be represented by a position-time graph as you have already learnt about it. Such a graph is a powerful tool to represent and analyse different aspects of motion of an object. For motion along a straight line, say X-axis, only x-coordinate varies with time and we have an x-t graph. Let us first consider the simple case in which an object is stationary, e.g. a car standing still at x = 40 m. The position-time graph is a straight line parallel to the time axis, as shown in Fig.

If an object moving along the straight line covers equal distances in equal intervals of time, it is said to be in uniform motion along a straight line.The following figure shows the position-time graph of such a motion.

Now, let us consider the motion of a car that starts from rest at time t = 0 s from the origin O and picks up speed till t = 10 s and thereafter moves with uniform speed till t = 18 s. Then the brakes are applied and the car stops at t = 20 s and x = 296 m. The position-time graph for this case is shown in Figure below.

Vector Concepts part two

This lesson is in continuation with Vectors concepts part one and going through that first will give more convenience to understand the present topic.

c)If three forces (vectors) are to be in equilibrium, then the sum of magnitudes of any two forces must be greater than the magnitude of third force.

d)Lami's theorem:

If a body is in equilibrium under the action of three coplanar forces P,Q,R at angles as shown in the figure,

18. A body of mass 'm' is suspended by a string of length 'l' from a rigid support. It is pulled aside by distance 'x' so that it makes an angle with the vertical by applying a horizontal force F. When the body is in equilibrium.

19. PARALLELOGRAM LAW OF VECTORS (OR FORCES):"If two vectors acting at a point making an angle with each other are represented both in magnitude and direction by the adjacent sides of a parallelogram, then the diagonal drawn from the same point will give the resultant both in magnitude and direction" .

22. POLYGON LAW OF VECTORS :" If number of vectors acting at a point in the same plane in different directions are represented both in magnitude and direction by the adjacent sides of a polygon taken in order, then the closing side taken in the reverse order will give the resultant both in magnitude and direction".

APPLICATIONS OF POLYGON LAW

1. If 'n' equal forces act on a body such that each force makes an angle 2∏ / n with the previous one and the polygon is closed, then the resultant is zero.

If each force of magnitude 'F' makes an angle Θ with previous one, then

a) the resultant is zero, if the number of forces is 2∏/ Θ

b) the resultant is 'F', if the number of forces are 2∏/ Θ - 1
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VECTORS CONCEPTS

1.Physical quantities are mainly classified into two types a) Scalars b) Vectors .

2. Scalar quantities re those which have only magnitude.

3. Physical quantities which have both magnitude and direction are called vectors and they should satisfy the parallelogram law of vector addition.

4. Mathematically any directed line segment is called a vector. It has three characteristics.

a) Support (base)
b) Sense (direction)
c) Length (mangnitude or modulus)

5. The magnitude of a vector is a scalar.

6. Electric current, velocity of light have both magnitude and direction but they do not obey the laws of vector addition. Hence they are scalars.

DIFFERENT TYPES OF VECTORS

7. EQUAL VECTORS: Two vectors are said to be equal when their magnitude and direction are equal.

8. NEGATIVE VECTOR: Negative vectors are those which are equal in magnitude but opposite in direction.

9. NULL VECTOR (ZERO VECTOR): It is a vector whose magnitude zero and direction is unspecified.

Examples :

a) Displacement after one complete revolution.

b) Velocity of vertically projected body at the highest point.

10. UNIT VECTOR : It is a vector whose magnitude is unity. A unit vector parallel to a given vector R is given by R ˆr = R

11. REAL VECTOR OR POLAR VECTOR : If the direction of a vector is independent of the coordinate system, then it is called a polar vector.

Example : linear velocity, linear momentum, force, etc.

12. PSEUDO VECTOR: Vectors associated with rotation about an axis and whose direction is changed when the co-ordinate system is changed from left to right, are called axial vectors (or) pseudo vectors.

Example : Torque, Angular momentum, Angular velocity, etc.

13. POSITION VECTOR: It is a vector that represents the position of a particle with respect to the origin of a co-ordinate system. The Position Vection of a point (x, y, z) is r = x i+yj+zk .

ADDITION OF VECTORS

14. There are three laws of addition of vectors.

a) Commutative law : A + B = B + A

b) Associative law : A + (B+C) = (A + B) + C

c) Distributive law : m(A + B) = mA + mB where m is a scalar

RESULTANT OF NUMBER OF VECTORS

15. Resultant is a single vector that gives the total effect of number of vectors.

16. Resultant can be found by using a) Triangle law of vectors b) Parallelogram law of vectors c) Polygon law of vectors .

17. TRIANGLE LAW OF VECTORS: If two given vectors are represented both in magnitude and direction by the two adjacent sides of a triangle, then closing side (third side) taken in the reverse order will give the resultant both in magnitude and direction.

APPLICATIONS OF TRIANGLE LAW :

a) MOTION OF A BOAT CROSSING THE RIVER IN SHORTEST TIME :

If velocities of boat and river are represented with B and R subscripts with V then to cross the river in shortest time, the boat is to be rowed across the river i.e., along normal to the banks of the river.

MOTION OF A BOAT CROSSING THE RIVER IN SHORTEST DISTANCE :

The previous post deals with UNITS AND DIMENSIONS OF PHYSICS PART TWO AND ONE.