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प्रश्न
Explain the phenomenon of self induction
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उत्तर
a. The phenomenon of production of an induced e.m.f in a coil due to change in current in the same coil is called self induction. It is also called as back-e.m.f.
b.
Consider a coil connected with battery E, plug key K and inductor L carrying current of magnitude I as shown in figure.
c. Since magnetic flux linked with the coil is directly proportional to the current,
∴ φ ∝ I
∴ φ = LI .…(i)
where, L = constant called coefficient of self induction or self inductance of the coil, which depends upon the number of turns, shape, area of the coil and material of the core.
d. Induced e.m.f in the coil is given by,
`e = -(dphi)/(dt)`
`e = − L (dI)/dt` ….(ii)
−ve sign in equation (ii) shows that self induced e.m.f opposes the rate of change of current.
`∴ |e| = |-L (dI)/dt|`
`∴ |e|= L (dI)/dt`
∴ Magnitude of self induced e.m.f is given by, `e = L (dI)/dt`
This is required induced e.m.f.
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संबंधित प्रश्न
Define self-inductance. Write its SI units.
The currents flowing in the two coils of self-inductance L1 = 16 mH and L2 = 12 mH are increasing at the same rate. If the power supplied to the two coil is equal, find the ratio of the currents ?
The currents flowing in the two coils of self-inductance L1 = 16 mH and L2 = 12 mH are increasing at the same rate. If the power supplied to the two coil is equal, find the ratio of the energies stored in the two coils at a given instant ?
Define self-inductance of a coil. Show that magnetic energy required to build up the current I in a coil of self inductance L is given by `1/2 LI^2`
A plot of magnetic flux (Φ) versus current (I) is shown in the figure for two inductors A and Β. Which of the two has larger value of self inductance?
Consider the self-inductance per unit length of a solenoid at its centre and that near its ends. Which of the two is greater?
A constant current i is maintained in a solenoid. Which of the following quantities will increase if an iron rod is inserted in the solenoid along its axis?
(a) magnetic field at the centre
(b) magnetic flux linked with the solenoid
(c) self-inductance of the solenoid
(d) rate of Joule heating.
An average emf of 20 V is induced in an inductor when the current in it is changed from 2.5 A in one direction to the same value in the opposite direction in 0.1 s. Find the self-inductance of the inductor.
A magnetic flux of 8 × 10−4 weber is linked with each turn of a 200-turn coil when there is an electric current of 4 A in it. Calculate the self-inductance of the coil.
What are the values of the self-induced emf in the circuit of the previous problem at the times indicated therein?
When a coil is connected to a D.C. source of e.m.f. 12 volt, then a current of 4 ampere flows in it. If the same coil is connected to a 12 volt, 25 cycle/s A.C sources, then the current flowing in it is 2.4 A. The self-inductance of the coil will be ______
Two rods of same material and volume having circular cross-section are subjected to tension T. Within the elastic limit, same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of first rod to second rod will be in the ratio
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The coefficient of self-inductance of a solenoid is 0.20 mH. If a core of soft iron of relative permeability 900 is inserted, then the coefficient of self-inductance will become nearly ______
The magnetic potential energy stored in a certain inductor is 15 mJ, when the current in the inductor is 40 mA. This inductor is of inductance ____________.
An e.m.f. of 10 volt is produced by a self inductance when the current changes at a steady rate from 6 A to 4 A in 1 millisecond. The value of self inductance is ____________.
Magnetic flux of 12 microweber is linked with a coil. When current of 3 mA flows through it, the self inductance of the coil is ____________.
A graph of magnetic flux `phi` versus current (I) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor ____________.
A graph of magnetic flux `(phi)` versus current (I) is shown for four inductors A, B, C and D. Larger value of self-inductance is for inductor ____________.
Two coils of self inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is ______.
Two solenoids of same cross-sectional area have their lengths and number of turns in ratio of 1 : 2 both. The ratio of self-inductance of two solenoids is ______.
When current i passes through an inductor of self-inductance L, energy stored in it is 1/2. L i2. This is stored in the ______.
A coil is wound on a frame of rectangular cross-section. If all the linear dimensions of the frame are increased by a factor 2 and the number of turns per unit length of the coil remains the same, self-inductance of the coil increases by a factor of ______.
The self-inductance associated with a coil is independent of ______.
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Energy needed to establish an alternating current I in a coil of self-inductance L is
A coil of wire of a certain radius has 600 turns and a self-inductance is 108 mH. The self-inductance of a second similar coil of 500 turns will be:
The self-inductance depends upon ______.
The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as ______.
The inductance of a solenoid L having diameter d. Let n be the number of turns per unit length. The inductance per unit length near the middle of a solenoid is ______.
(Assume that, l = current passes through the turns, µ0 = Permeability of vacuum)
A toroid of a circular cross-section of radius 0.05 m has 2000 windings and a self-inductance of 0.04 H. What is (a) the current through the windings when the energy in its magnetic field is 2 × 10−6 J and (b) the central radius of the toroid?
The current flowing through an inductor of self-inductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses dI/dt is shown graphically by figure
Two inductor coils with inductance 5 mH and 15 mH are connected in parallel. The resultant inductance of the combination of the two coils is ______.
Which ratio defines the self-inductance of a coil using magnetic flux linkage?
What does \[L\] represent?
What does \[\Phi_B\] represent, and what is its SI unit?
What does \[I\] represent, and what is its SI unit?
Which set gives equivalent units for one henry?
Which set of quantities describes the long solenoid used to derive its self-inductance?
For an air (or vacuum) core, which permeability is used in the solenoid derivation?
What is the magnetic field inside a long air-core solenoid?
What is the magnetic flux through one turn of the long solenoid?
Before substituting \[N=nl\], what is the total flux linkage through all \[N\] turns?
When current builds up from zero to \[I\] in an inductor, work is done against what?
In which field is the energy of an inductor stored?
Using \[B=\mu_0nI\], what is the magnetic energy density inside the air-core solenoid?
