Root Mean square value of AC

  • We know that time average value of AC over one cycle is zero and it can be proved easily
  • Instantaneous current I and time average of AC over half cycle could be positive for one half cycle and negative for another half cycle but quantity i2 would always remain positive 
  • So time average of quantity i2 is

    This is known as the mean square current
  • The square root of mean square current is called root mean square current or rms current.

    thus ,the rms value of AC is .707i0 of the peak value of alternating current
  • Similarly rms value of alternating voltage or emf is

  • If we allow the AC current represented by i=i0sin(ωt+φ) to pass through a resistor of resistance R,the power dissipated due to flow of current would be
  • Since magnitude of current changes with time ,the power dissipation in circuit also changes
  • The average Power dissipated over one complete current cycle would be

    If we pass direct current of magnitude irms through the resistor ,the power dissipate or rate of production of heat in this case would be
  • Thus rms value of AC is that value of steady current which would dissipate the same amount of power in a given resistance in a given tine as would gave been dissipated by alternating current
  • This is why rms value of AC is also known as virtual value of current

What is center of mass?

  • Consider a body consisting of large number of particles whose mass is equal to the total mass of all the particles. When such a body undergoes a translational motion the displacement is produced in each and every particle of the body with respect to their original position.
  • If this body is executing motion under the effect of some external forces acting on it then it has been found that there is a point in the system , where if whole mass of the system is supposed to be concentrated and the nature the motion executed by the system remains unaltered when force acting on the system is directly applied to this point. Such a point of the system is called centre of mass of the system.
  • Hence for any system Centre of mass is the point where whole mass of the system can be supposed to be concentrated and motion of the system can be defined in terms of the centre of mass.
  • Consider a stationary frame of refrance where a body of mass M is situated. This body is made up of n number of particles. Let mi be the mass and ri be the pisition vector of i'th particle of the body.
  • Let C be any point in the body whose position vector with respect to origin O of the frame of refrance is Rc and position vector of point C w.r.t. i'th particle is rci as shown below in the figure.

  • From triangle OCP
    ri=Rc+rci                               (1)
    multiplying both sides of equation 1 bt mi we get
    taking summation of above equation for n particles we get

    If for a body

    then point C is known as the centre of mass of the body.
  • Hence a point in a body w.r.t. which the sum of the product of mass of the particle and their position vector is equal to zero is equal to zero is known as centre of mass of the body.

Career opportunities in physics and engineering

Majority of students studying in senior school find physics as a more difficult subject. They find difficult to gasp various theories and formulas of physics. Physics is the most fundamental of all natural sciences and it describes how nature works using the language of mathematics. Now a question arises why should a student opt to study physics when he can choose between number of other branches of science that are much easy to study and understand. I would say before opting for physics a student needs to know why the physics is important and what career options a student may get out of studying physics at senior school.
Physics is the most basic natural science. The name physics comes from the ancient Greek word for nature. And the name fits perfectly: Physics deals with everything that occurs in nature, may it be in atoms, cars, semiconductors or outer space. This all belongs to physics.  Physics tries to explain natures by models. These are theoretical constructs, written in the language of logic, mathematics. Models can be falsified by experiments that show different outcome than expected, they cannot be verified.
To know the importance of physics in your daily life look around yourself and see how our daily life relies on technology, for example most of the electronic devices which are now important part of our life use transistors which came into existence due to research on physics of semiconductors and semiconductor devices and you can find lots of examples like this. Physics is an important subject to learn and understand if you are planning to make a career in medical sciences, engineering or technology. For example in case of medical sciences physics supplements a lot when it comes to be about branches like radiology.
In case of engineering studying and understanding physics becomes further more important as every branch of engineering be it electrical, mechanical or mechanical involves application of physics. The basic concepts we learn in physics play an important role in understanding complex scenarios in engineering. There are lots of career opportunities in engineering degree and if you want to opt engineering as an career option you can visit Online Engineering Degree for detailed information about different branches of engineering.
Further if you do not want to go for medical or engineering you can also opt to become a research scientist, teacher, lecturer or professor in physics. For this you would need to physics as a subject to study during graduation then go for post graduation and even have to go for a PhD degree in physics. So you see there are  lots of career opportunities for a student interested in physics and there are so many reasons why you should study physics.

Uniformly accelerated motion

Electric Field

Student with basic knowledge of electrostatics must have studied about electric field in many books with no proper definition in most of the books. But what exactly is electric field which is only said to be existed in any region in which electric force is said to be existed and this question is not the easiest one to answer. It was Michael Faraday who first referred to an electric ‘‘field of force,’’ and James Clerk Maxwell identified that field as the space around an electrified object – a space in which electric forces act. We all know that electric field and force are closely related and most basic definition of electric field is the electric force per unit area acting on the charged object.
where this charge q is often known as test charge.
Since electric field in general is altered by the presence of test charge
E = lim Δq 0 ΔF Δq = dF dq
So, it is clear from above discussion that 

(1) E is a vector quantity with magnitude directly proportional to force and with direction given by the direction of the force on a positive test charge.
(2) E has units of newtons per coulomb (N/C)
While applying Gauss's law it is helpful to visualize electric field near charged object and the most common
approach is  to construct a visual representation of an electric field which is to use a either arrows or ‘‘field lines’' that point in the direction of the field at each point in space as shown below

  • So, electric field line is an imaginary line drawn in such a way that it's direction at any point is same as the direction of field at that point.
  • An electric field line is, in general a curve drawn in such a way that the tangent to it ateach point is the direction of net field at that point.
  • Field lines of a single position charge points radially outwards while that of a negative charge are radially inwards as shown below in the figure.

  • Field lines around the system of two positive charges gives a different picture and describe the mutual repulsion between them.

  • Field lines around a system of a positive and negative charge clearly shows the mutual attraction between them as shown below in the figure.

  • Some important general properties of field lines are
    1.Field lines start from positive charge and end on a negative charge.
    2.Field lines never cross each other if they do so then at the point of intersection there will be two direction of electric field.
    3.Electric field lines do not pass through a conductor , this shows that electric field inside a conductor is always zero.
    4.Electric field lines are continuous curves in a charge free region.

  • I would like to say that you can think of electric field as a quantity filling the space in the neighborhood of an electric charge. The electric-field concept helps us understand not only the forces between isolated stationary charged bodies but also what happens when charges move. When charges move, their motion is communicated to neighboring charged bodies in the form of a field disturbance.

    position, distance and displacement

    How to draw a free body diagram

    1. First create a mental picture of the body for which you want to write momentum balance equation.
    2. Draw rough sketch of your system showing it to be isolated from its environment.
    3. Place a dot in the center of the object and at this point all the forces are assumed to be acting upon.
    4. For every force acting on that body , draw a vector which shows size and direction of the force. each vector should start at the dot. 
    5. Label each vector based on the type of force and remember not to include numbers and calculations

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