Derived Formula & Unit Of Potential difference : -
Potential Difference (P.D.) = Work Done / Charged Moved = W/Q = Joule/ Coulomb = Volt.
If electric charge flows through some region, say a wire of copper, we say that there is an electric current in that region. e. g. through the copper wire.
Electric current, namely the flow of electric charge, can be described by the amount of charge flowing through a particular area in a unit time, or as the rate of passes through a given cross section or a area in a short time t . The electric current I (or current ) is given by
I = lim
t -->0 (Q / t ) = dQ / dt. SI Unit
1 Ampere = 1 Coulomb / second Measurement of Current
A Magnetic field ( or Magnetic flux ) that changes with time produces an emf or Voltage. The emf is exactly equal to the potential difference between its ends.
Symbol
When a source of emf is connected to a wire of any other object (called conductor) allowing the passage of electric charge, there is a voltage drop V across the conductor and a steady or direct current (say I) flows through it (and source of emf ). The ratio of the two, namely ( V / I ) is called the electric resistance of the conductor. SI Unit
Electric resistance is the ratio of one volt and one ampere. Or We can say that Ohm is the unit of Electric resistance.
Definition :-
Imagine two or more resistors in series, i.e. connected one after another so that the same current flows through them. The total resistance of the collection is the sum of individual resistances.
Suppose a current i flows through the resistances. The potential difference V between the points P and Q is the sum of voltage differences across the sequence of resistors, i.e., i( R1 + R2 + R3 +.............+ Rn ), and the current flowing is i, so that the resistance is
( V / i ) = R = R1 + R2 + R3 + .............. + Rn .......................(1)
This is the well known formula for the total resistance of n resistors in series.
In the given figure, we show 3 resistors connected 'in parallel' with one another. In this case, the current flowing into P is divided among the 3 resistors:
i = i1 + i2 + i3
However, the potential difference across any resistors is the same, namely
i1 R1 = i2 R2 = 13 R3
These equations can be thought of as determining the currents i1, i2, i3.
Substituting, We have
i = ( V/R1 + V/R2 + V/R3 ) = V / R
or
1/R1 + 1/R2 + 1/R3 = 1 / R.
Similarly, For n number of resistors connected in parallel,
The Total Equivalent resistance = 1/R1 + 1/ R2 +.......+ 1/Rn = 1 / R.
Kirchhoff's laws are particularly useful:
(a) in determining the equivalent resistance of a complicated network of conductors and
(b) for calculating the current flowing in the various conductors.
The two laws are :
Point law or current law (KCL) :-
In any electrical network, the algebraic sum of the currents meeting at a point (or junction ) is zero.
i.e. the total current leaving a junction is equal to the total current entering that junction.
(a)
Assuming the incoming current to be positive and the outgoing currents negative, we have
I1 + ( - I2 ) + ( - I3 ) + I4 + (- I5) = 0
Or I1 - I2 - I3 + I4 - I5 = 0
Or I1 + I4 = I2 + I3 + I5
Or Incoming currents = Outgoing Currents
We express the above conclusion thus
n
∑ Ij = 0 ........................at a junction
j=1
Mesh Law or Voltage Law (KVL) :-
The algebraic sum of the products of currents and resistance in each of the conductors in any closed path ( or mesh ) in a network plus the algebraic sum of the e.m.fs. in that path is zero.
In other words,
∑ I R + ∑ e. m. f. = 0 .............................round a mesh
If one starts from a particular junction and goes round the mesh till one comes back to the starting point, then one must be at the same potential with which one started. Hence, it means that all the sources of e. m. f. meet on the way must necessarily be equal to the voltage drops in the resistance, every voltage being given its proper sign, plus or minus.
Whenever an electric current flows through a conductor, a magnetic field is immediately brought into existence in the space surrounding the conductor. It can be said that when electrons are in motion, they produce a magnetic field. The converse is also true i.e. when a magnetic field embracing a conductor moves relative to the conductor, it produce a flow of electrons in the conductor. This phenomenon whereby an e.m.f. and hence current is induced in any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic induction.
First Law :
Whenever the magnetic flux linked with a circuit changes, an e.m.f. is always induced in it.
or
Whenever a conductor cuts magnetic flux, an e.m.f. is induced in that conductor.
Second Law :
The magnitude of the induced e.m.f. is equal to the rate of change of flux linkages.
Explanation | Faraday's Experiment | Direction of induced emf | Lenz's law
The direction of induced current may be found easily by applying either Fleming's Right-hand Rule or Lenz's Law
Electromagnetically induced current always flows in such direction that the action of the magnetic field set up by it tends to oppose the very cause which produces it.
Definition :
Electromagnetically induced current always flows in such direction that the action of the magnetic field set up by it tends to oppose the very cause which produce it.
Ohms Law
In 1828, George Simon Ohm, a German physicist, found that for many substances, the electrical current I flowing through them is proportional to the voltage V across their ends.
The empirical relationship
V µ I
is called Ohm's Law. The constant of proportionality, called the resistance and given the symbol R, is independent of V or I, but depends only on the substances and its shape and size. Thus Ohm's Law is
V = R * I
Unit of Resistance:-
Volt per ampere OR Ohm ( W )
An electric motor is a machine which converts electrical energy into mechanical energy.
Principle:
It is based on the principle that when a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force whose direction is given by Fleming's Left-hand rule and whose magnitude is given by
Force, F = B I l newton
Where B is the magnetic field in weber/m2.
I is the current in amperes and
l is the length of the coil in meter.
The force, current and the magnetic field are all in different directions.
If an Electric current flows through two copper wires that are between the poles of a magnet, an upward force will move one wire up and a downward force will move the other wire down.
Figure 1: Force in DC Motor
Figure 2 : Magnetic Field in DC Motor
Figure 3 : Torque in DC Motor
Figure 4 : Current Flow in DC Motor
The loop can be made to spin by fixing a half circle of copper which is known as commutator, to each end of the loop. Current is passed into and out of the loop by brushes that press onto the strips. The brushes do not go round so the wire do not get twisted. This arrangement also makes sure that the current always passes down on the right and back on the left so that the rotation continues. This is how a simple Electric motor is made.
An electrical Generator is a machine which converts mechanical energy (or power) into electrical energy (or power).
Principle :
It is based on the principle of production of dynamically (or motionally) induced e.m.f (Electromotive Force). Whenever a conductor cuts magnetic flux, dynamically induced e.m.f. is produced in it according to Faraday's Laws of Electromagnetic Induction. This e.m.f. causes a current to flow if the conductor circuit is closed.
Hence, the basic essential parts of an electric generator are :
A magnetic field and
A conductor or conductors which can so move as to cut the flux.
Construction :
A single-turn rectangular copper coil abcd moving about its own axis in a magnetic field provided by either permanent magnets or electromagnets. The two ends of the coil are joined to two split-rings which are insulated from each other and from the central shaft. Two collecting brushes (of carbon or copper) press against the slip rings.
Principle :
A.C. generators or alternators (as they are usually called) operate on the same fundamental principles of electromagnetic induction as D.C. generators.
Alternating voltage may be generated by rotating a coil in the magnetic field or by rotating a magnetic field within a stationary coil. The value of the voltage generated depends on-
the number of turns in the coil.
strength of the field.
the speed at which the coil or magnetic field rotates.
A transformer is a static piece of apparatus by means of which electric power in one circuit is transformed into electric power of the same frequency in another circuit. It can raise or lower the voltage in a circuit but with a corresponding decrease or increase in current.