Advertisements
Advertisements
प्रश्न
An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10−3 s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.
Advertisements
उत्तर
Length of the solenoid, l = 30 cm = 0.3 m
Area of cross-section, A = 25 cm2 = 25 × 10−4 m2
Number of turns on the solenoid, N = 500
Current in the solenoid, I = 2.5 A
Current flows for time, t = 10−3 s
Average back emf, `"e" = ("d"phi)/("dt")` .........(1)
Where,
`"d"phi` = Change in flux = NAB …........(2)
Where,
B = Magnetic field strength = `mu_0("NI")/"l"` ......(3)
Where,
`mu_0` = Permeability of free space = 4π × 10−7 T m A−1
Using equations (2) and (3) in equation (1), we get
e = `(mu_0"N"^2"IA")/("lt")`
= `(4pi xx 10^-7 xx (500)^2 xx 2.5 xx 25 xx 10^-4)/(0.3 xx 10^-3)`
= 6.5 V
Hence, the average back emf induced in the solenoid is 6.5 V.
संबंधित प्रश्न
Explain the meaning of the term mutual inductance.
In an experiment, two coils c1 and c2 are placed close to each other. Find out the expression for the emf induced in the coil c1 due to a change in the current through the coil c2.
A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s−1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
A coil of self-inductance 2.5H and resistance 20Ω is connected to a battery of emf 120V having the internal resistance of 5 n. Find:
1) The time constant of the circuit.
2) The current in the circuit in steady state
Find the mutual inductance between the straight wire and the square loop of figure.
A pair of the adjacent coil has a mutual inductance of 1.5 H. If the current in one coil varies from 0 to 20 A in 0.5 s, what is the change of flux linked with the other coil.
In mutual induction, the main current remains same because ____________.
A current I = 10 sin (50 π t) ampere is passed in the first coil which induces a maximum e.m.f. of 5 π volt in the second coil. The mutual inductance between the coils is ______.
Alternating current of peak value `(2/pi)` ampere flows through the primary coil of transformer. The coefficient of mutual inductance between primary and secondary coil is 1 H. The peak e.m.f. induced in secondary coil is ______. (Frequency of a.c. = 50 Hz)
The mutual inductance between two coplanar concentric rings A and B of radii 'R1' and 'R2' placed in air when a current 'I' flows through ring A is (R1 >> R2) (µ0 = permeability of free space) ____________.
Two coils P and Q have mutual inductance 'M' H. If the current in the primary is I = I0 sin `omega`t, then the maximum vlaue of e.m.f. indued in coil Q is ____________.
The mutual inductance between two coils is 0.09 henry. If the current in the primary coil changes from 0 to 20 A in 0.006 s, the e.m.f. induced in the secondary coil at that instant is ____________.
If number of turns in primary and secondary coils is increased to two times each, the mutual inductance ______.
Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to ______.
Write the S.I. unit of mutual inductance.
State and define the SI unit of mutual inductance.
