Advertisements
Advertisements
प्रश्न
Explain the phenomenon of self induction
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.
APPEARS IN
संबंधित प्रश्न
In a given coil of self-inductance of 5 mH, current changes from 4 A to 1 A in 30 ms. Calculate the emf induced in the coil.
Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.
Define the coefficient of self-induction.
Define self-inductance. Write its SI units.
A toroidal solenoid with air core has an average radius of 15 cm, area of cross-section 12 cm2 and has 1200 turns. Calculate the self-inductance of the toroid. Assume the field to be uniform across the cross-section of the toroid.
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?
Define self inductance. Write its S.I. units.
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.
An inductor-coil carries a steady-state current of 2.0 A when connected across an ideal battery of emf 4.0 V. If its inductance is 1.0 H, find the time constant of the circuit.
A coil having inductance 2.0 H and resistance 20 Ω is connected to a battery of emf 4.0 V. Find (a) the current at the instant 0.20 s after the connection is made and (b) the magnetic field energy at this instant.
Consider a small cube of volume 1 mm3 at the centre of a circular loop of radius 10 cm carrying a current of 4 A. Find the magnetic energy stored inside the cube.
Explain why the inductance of two coils connected in parallel is less than the inductance of either coil.
Two pure inductors each of self-inductance L are connected in series, the net inductance is ______
Obtain an expression for the self-inductance of a solenoid.
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
When the number of turns in a coil is tripled without any change in the length of the coil, its self-inductance ______
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 ______
Consider a solenoid carrying supplied by a source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will ______.
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 resistance of 100 `Omega`, inductor of self-inductance`(4/pi^2)` H and a capacitor of unknown capacitance are connected in series to an a.c. source of 200 V and 50 Hz. When the current and voltage are in phase, the capacitance and power dissipated is respectively ____________.
The frequency of γ-rays, X-rays and ultraviolet rays are a, b and c respectively. Then, ______.
When the current in a coil changes from 2 amp. to 4 amp. in 0.05 sec., an e.m.f. of 8 volt is induced in the coil. The coefficient of self inductance of the coil 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 ______.
The self-inductance associated with a coil is independent of ______.
An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 800, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10-3s. Ignoring the variation in magnetic field near the ends of the solenoid, the average back emf induced across the ends of the open switch in the circuit would be ______.
If both the number of turns and core length of an inductor is doubled keeping other factors constant, then its self-inductance will be ______.
Energy needed to establish an alternating current I in a coil of self-inductance L is
An inductor may store energy in
What is the unit of self-inductance of a coil?
An average induced emf of 0.20 V appears in a coil when the current in it is changed from 5A in one direction to 5A in the opposite direction in 0.20 sec. Find the self induction of the coil.
In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ______.
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 current of 1A flows through a coil when it is connected across a DC battery of 100V. If the DC battery is replaced by an AC source of 100 V and angular frequency of 100 rad s-1, the current reduces to 0.5 A. Find
- the impedance of the circuit.
- self-inductance of coil.
- Phase difference between the voltage and the current.
Obtain an expression for the self inductance of a solenoid.
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?
What is meant by magnetic coupling coefficient?
