Monday, 23 September 2013
Shunt
A shunt is a device which allows electric current to pass around another point in the circuit by creating a low resistance path.
Force on a Current Carrying Conductor Placed in a Magnetic Field
Force experienced by each electron in the conductor is
If n be the number density of electrons, A be the area of cross section of the conductor, then no. of electrons in the element dl is nAdl. Force experienced by the electrons in dl is
Lorentz Force
A current carrying conductor placed in a magnetic field experiences a force which means that a moving charge in a magnetic field experiences force.
Special Cases:
i) If the charge is at rest, i.e. v = 0, then Fm = 0. So, a stationary charge in a magnetic field does
not experience any force.
ii) If θ = 0°or 180°i.e. if the charge moves parallel or anti-parallel to the direction of the magnetic
field, then Fm = 0.
iii) If θ = 90°i.e. if the charge moves perpendicular to the magnetic field, then the force is
maximum. Fm (max) = q v B
Differences Between Biot Savart’s Law And Coulomb’s Law
1. E is produced by a scalar source (q) where as B is produce by vector source (Idl)
2. E is acting along the displacement vector where as B acts perpendicular to Ixr.
3. E is not depended of θ where as B depends upon θ.
Similarity Between Biot Savart’s Law And Coulomb’s Law
1. Field at any point vary inversely as the square of the distance
2. Both obey superposition principle
3. The magnetic fields linear in the source just as electric field
Magnetic Field
If a charged particle is projected in a magnetic field, in general, it experiences a magnetic force. By projecting the particle in different direction from the same point P with different speeds, we can observe the following facts about the magnetic field force.
a. Force experienced by the moving charge is directly proportional to the magnitude of the charge i.e.
F α q
b. Force experienced by the moving charge is directly proportional to the component of velocity perpendicular to the direction of magnetic field i.e.
F α v sinθ
c. The magnitude of the force F is directly proportional to the magnitude of the magnetic field applied i.e.
F α B
On combining all factors we get,
F = kq v sinθ B
Here k=1 is proportionality constant. F= q v sinθ B. Here we can see that v and B follows the vector product hence force is perpendicular to v and B. Direction of the force can be can by Right Handed Screw Rule or Right Hand Rule.
By measuring the magnetic force F acting on a charge q moving at a speed v, we can obtain B. If v=1, q=1 and sinθ =1 or θ=90º thenF = 1x 1x B x 1 =B
Thus the magnetic field induction at a point in the field is equal to the force experienced by a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point.
Special Cases
a. If θ =0º or 180º the F = q v Bsin(0) = 0. Its means, a charged particle moving parallel to the direction of magnetic field, does not experience any force.
b. If θ =90º or 180º the F = q v Bsin(90) = qvB (maximum force). Its means, a charged particle moving along a perpendicular to the direction of magnetic field, it experiences maximum force.
c. If v =0, then F=q v sinθ B = 0. It means, a charged particle is at rest in a magnetic field, it experiences maximum force. It experiences no force.
UNIT OF MAGNETIC FIELD B
SI unit of magnetic field is tesla (T) or Weber /meter2
1T = 1NA-1m-1
1 Gauss = 10-4 T
Dimensions of B = [MA-1T-2]
We have a magnetic field of the order of 10-5 T near to earth surface
Magnetic field is also called as Magnetic Induction or Magnetic Flux Density.
Ampere’s Swimming Rule
According to this rule, if we imagine a man swimming along current direction in wire such that current enters from feet and leaves from the head, then the N-pole deflected towards his left hand.
Oersted's Experiment
Take a magnetic needle NS, which can rotate freely about a vertical axis in horizontal plane. Hold a conducting wire AB over the magnetic needle NS parallel to it. Complete the circuit by closing the key such that current flows from A to B.
It is found that N-pole of the magnetic needle gets deflected the west. If the direction of current in the wire is reversed (i.e. from B to A), the N-pole of magnetic needle gets deflected towards east. Since magnetic needle can be deflected by another magnetic field therefore current in the wire must be producing a magnetic field in the surrounding space.
Introduction - Magnetic Field
If a charge q is placed at rest at a point P near a metallic wire carrying a current I, it experience almost no force. We conclude that there s no appreciable electric field at the point P. This is expected because in any volume of wire (which contains several thousand atoms) there are equal amount of positive and negative charges. The wire is electrically neutral and does not produce an electric field.
(In fact, there is small charge density on the surface of the wire which does produce an electric field near the wire. This field is very small and can be neglected.)
However, if the charge q is projected from point P in the direction of current, it is deflected towards the wire (q is assume to be positive). There must be a field which exerts a force on charge when it is projected, but not when it is kept at rest. This field is calledMagnetic Field.
The branch of physics which deals with the magnetism due to electric current is called electromagnetism.
Some result of experiments for the magnetic field due to a straight long current-carrying wires are shown below. The wire is perpendicular to the plane of the paper. A ring of compass needles surrounds the wire. The orientation of the needles is shown when
Introduction - Magnetic Field
If a charge q is placed at rest at a point P near a metallic wire carrying a current I, it experience almost no force. We conclude that there s no appreciable electric field at the point P. This is expected because in any volume of wire (which contains several thousand atoms) there are equal amount of positive and negative charges. The wire is electrically neutral and does not produce an electric field.
(In fact, there is small charge density on the surface of the wire which does produce an electric field near the wire. This field is very small and can be neglected.)
However, if the charge q is projected from point P in the direction of current, it is deflected towards the wire (q is assume to be positive). There must be a field which exerts a force on charge when it is projected, but not when it is kept at rest. This field is calledMagnetic Field.
The branch of physics which deals with the magnetism due to electric current is called electromagnetism.
Some result of experiments for the magnetic field due to a straight long current-carrying wires are shown below. The wire is perpendicular to the plane of the paper. A ring of compass needles surrounds the wire. The orientation of the needles is shown when
Maximum Power Transfer Theorem
It states that the power output across the load due to a cell or battery, is maximum if the load resistance is equal to the effective internal resistance of a cell or battery.
Maximum Power Transfer Theorem
It states that the power output across the load due to a cell or battery, is maximum if the load resistance is equal to the effective internal resistance of a cell or battery.
Maximum Power Transfer Theorem
It states that the power output across the load due to a cell or battery, is maximum if the load resistance is equal to the effective internal resistance of a cell or battery.
Some Effect of Heating Effect of Currents
The wires supplying current to an electric lamp are not practically heated while that of the filament of lamp becomes white hot. Wire has very less resistance but filament has higher resistance. Heating is proportional to R.
Nichrome wire (alloy of Ni and Cr): it has high melting point and high value of specific resistance.
ii. It can be easily drawn
iii. It is not oxidized easily when heated in air
Resistance of high electric power instruments is smaller than that of low electric power.
Fuse wire is generally prepared by tin-lead alloy. It should have high resistivity, low melting point and of suitable current rating. Fuse wire is used in series with electrical installation.
Efficiency of an electric device (η)
η = output power/input power
For electric motor, η = output mechanical power/input electric power, input electric power =output mechanical power + power lost in heat.
Electric Energy
The electric energy consumed in a circuit is defined as the total work done in maintaining the current in an electric circuit for a given time.
Electric Energy =VIt=I2Rt= V2/Rt=P.t
SI unit is Joule, also 1 joule = watt-second
Commercial unit of electric energy is kilowatt hour (kWh) or Board of trade unit (B.O.T.U) or UNIT of electricity
1kWh=1000watt x 1 hours = 1000watt x 60min x 60s=3.6x106 J
No. of units of electricity consumed = watt-hour/1000
Electric Power
The rate at which electric work is done by the source of emf in maintaining the current in electric circuit
W=VIt
Therefore Electric Power (P) = W/t =VIt/t=VI watt or joule/s
Power is said to be one watt if one ampere of current flows I it against a potential difference of 1 volt
Commercial unit of power is horse power, 1HP=746watt
P=VI=I2R=V2/R
It is the chemical energy of cell which supplies the power to the circuit.
Heat Produced by electric Current
Consider a conductor of resistance R, potential difference across it V and I is current flowing for some time t.
Total charge flow from one end to other q = It. Also work done in carry a charge from one end to other of conductor is
W=Potential difference x charge = Vq = VIt =I2Rt joules.
I2Rt is called electric work done which appears as heat.
H=W= I2Rt joules = I2Rt/4.18 calories.
Joule heating effect is irreversible. If direction of current changed it will not produce cooling but heat only.
Heating effects of Current: Joule's Effect
Whenever electric current passed through a conductor, it becomes hot after a certain time. This effect of getting hot by conductor is called as heating effect of current; Joule’s Law.
Amount of heat produced (H) when a current I flows through a conductor of resistance R for a time t is given by
H α I2Rt …… known as joule’s law of heating.
When potential difference is applied across the conductor, E produced due to this potential exerts the force on electrons. Electrons gain kinetic energy and loss it when collide in between. This lost energy rise the temperature of the ion or atoms. Hence temperature of conductor increased.
E.m.f. of cell converts into the heat energy of conductor.
Sensitiveness of Potentiometer
Its means is the smallest potential difference can be measured with the help of Potentiometer. Sensitivity of Potentiometer can be increased by decreasing its potential gradient. The same can be achieved by
1. By increasing the length of potentiometer wire.
2. If the potentiometer wire is a fixed length, the potential gradient can be deceased by reducing the current in the potentiometer wire circuit with help of rheostat.
Determnation of Internal Resisitance of a cell by Potentiometer Method
A battery of emf ε is connected the end terminal A and B of potentiometer wire with rheostat Rh, and key K in series. This is called an auxiliary circuit. Cell of emf which to be measure is connected as shown in the figure.
Now we find the no deflection position of galvanometer by closing the key K. we get
ε=Kl1 …..1
Now we close the key K1, resistance R is also added in circuit and we find the no deflection position of galvanometer at l2 therefore
V= Kl2 …..2
Divide 1by 2 we get
ε/ V= l1/l2 …..3
We know that the internal resistance r1 of a cell of emf E, when resistance R connected in its circuit is given by
r1 = (ε-V) R/ V = (ε/ V-1) R …..4
Putting the value from 3 to 4, we get
r1 = (l1/l2 -1) R
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