Advertisements
Advertisements
प्रश्न
Obtain an expression for the self-inductance of a solenoid.
Advertisements
उत्तर
- Consider a current I established in the windings (turns) of a long solenoid. The current produces a magnetic flux `phi_"B"` through the central region.
- The inductance of the solenoid is given by,
L = `("N"phi_"B")/"I",`
where N = the number of turns,
ΦB = magnetic flux linkage. - The flux linkage for a length l near the middle of the solenoid is,
NΦB = (nl) `(vec"B". vec"A")` = nlBA, (for θ = 0°),
where n = the number of turns per unit length,
B = magnetic field
A = the cross-sectional area of the solenoid. - The magnetic field inside the solenoid is given as, B = `mu_0"ni"`
- Hence, L = `("N"phi_"B")/"i"`
= `(("nl")"BA")/"i"`
= `("nl"(mu_0"ni")"A")/"i"`
∴ L = μ0n2lA
where, Al is the interior volume of solenoid.
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.
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.
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 ?
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`
Derive the expression for the self-inductance of a long solenoid of cross sectional area A and length l, having n turns per unit length.
Derive an expression for self inductance of a long solenoid of length l, cross-sectional area A having N number of turns.
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.
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.
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.
A long wire carries a current of 4.00 A. Find the energy stored in the magnetic field inside a volume of 1.00 mm3 at a distance of 10.0 cm from the wire.
Answer the following question.
When an inductor is connected to a 200 V dc voltage, a current at 1A flows through it. When the same inductor is connected to a 200 V, 50 Hz ac source, only 0.5 A current flows. Explain, why? Also, calculate the self-inductance of the inductor.
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 ______
A coil of self-inductance 3 H carries a steady current of 2 A. What is the energy stored in the magnetic field of the coil?
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
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 ____________.
Two coils of wire A and B are placed mutually perpendicular as shown. When current is changed in any one coil.
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 coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when ____________.
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 ____________.
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 ______.
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?
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:
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.
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 ______.
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)
Calculate the self-inductance of a coil using the following data obtained when an AC source of frequency `(200/pi)` Hz and a DC source are applied across the coil.
| AC Source | ||
| S.No. | V (volts) | I (A) |
| 1 | 3.0 | 0.5 |
| 2 | 6.0 | 1.0 |
| 3 | 9.0 | 1.5 |
| DC Source | ||
| S.No. | V (volts) | I (A) |
| 1 | 4.0 | 1.0 |
| 2 | 6.0 | 1.5 |
| 3 | 8.0 | 2.0 |
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?
