Advertisements
Advertisements
Question
The mutual inductance of two coils is 10 mH. If the current in one of the coil changes from 5 A to 1 A in 0.2 s, calculate the emf induced in the other coil. Also calculate the induced charge flowing through the coil if its resistance is 5 Ω.
Solution
Data: M = 10 mH = 10-2 H, I1i = 5 A, I1f = 1 A, Δ t = 0.2 s, R = 5 Ω
The mutually induced emf in coil 2 due to the changing current in coil 1,
`"e"_21 = - "M" (triangle "I"_1)/(triangle "t") = - "M" ("I"_(1"f") - "I"_(1"i"))/(triangle "t")`
`= - (10^-2)((1 - 5)/0.2)` = 0.2 V
If ΔQ2 is the charge that flows through coil 2 due to the changing current in coil 1, the induced current in coil 2 is
`"I"_2 = (triangle "Q"_2)/(triangle "t") = "e"_2/"R"_2`
∴ ΔQ2 = `"e"_2/"R"_2 triangle "t" = 0.2/5 (0.2) = 0.04/5`
= 0.008 C = 8 mC
APPEARS IN
RELATED QUESTIONS
If the radius of a sphere is doubled without changing the charge on it, then electric flux originating from the sphere is ______.
Explain the meaning of the term mutual inductance.
The current flowing through an inductor of self inductance L is continuously increasing. Plot a graph showing the variation of Magnetic potential energy stored versus the current.
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?
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.
Define coefficient of mutual induction.
Consider two concentric circular coils, one of radius r1 and the other of radius r2 (r1 < r2) placed coaxially with centers coinciding with each other. Obtain the expression for the mutual inductance of the arrangement.
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
Two circular loops are placed with their centres separated by a fixed distance. How would you orient the loops to have (a) the largest mutual inductance (b) the smallest mutual inductance?
Find the mutual inductance between the straight wire and the square loop of figure.
Find the mutual inductance between the circular coil and the loop shown in figure.
The current in a long solenoid of radius R and having n turns per unit length is given by i= i0 sin ωt. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid ant the coil.
A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 10 A in 0.2 s, what is the change of flux linkage with the other coil?
An emf of 96.0 mV is induced in the windings of a coil when the current in a nearby coil is increasing at the rate of 1.20 A/s. What is the mutual inductance (M) of the two coils?
A long solenoid of length l, cross-sectional area A and having N1 turns (primary coil), has a small coil of N2 turns (secondary coil) wound about its center. Determine the Mutual inductance (M) of the two coils.
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.
Define Mutual Inductance.
The dimensions of self or mutual inductance are given as ______.
In an induction coil, the coefficient of mutual inductance is 6 henry. If a current of 10 ampere in the primary coil is cut-off in `1/1500"s"`, the e.m.f. at the terminals of the secondary coil will be ____________.
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 ______.
An alternating current of frequency 200 rad/s and peak value 1 A is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is 1.5H, then the voltage induced in the secondary will be approximately (π = 2217)
A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. (R>>r) if both the coils are coplanar then the mutual inductance between them is proportional to ______.
Two different wire loops are concentric and lie in the same plane. The current in the outer loop (I) is clockwise and increases with time. The induced current in the inner loop.
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 ____________.
The coefficient of mutual inductance is 2H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A and 3A. The time required for the change of current is ____________.
Two circular coils have their centres at the same point. The mutual inductance between them will be maximum when their axes ______
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 ______.
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 ______.
There are two coils A and B seperated by some distance. If a current of 2A flows through A, a magnetic flux of 10-2 Wb passes through B (no current through B). If no current passes through A and a current of 1A passes through B, what is the flux through A?
An emf of 91 mV is induced in the windings of a coil when the current in o nearby coil is increasing at the rate of 1.3 A/s. what is the mutual inductance (M) of the two coils in mH?
A toroid is a long coil of wire wound over a circular core. The major radius and cross-sectional radius of the toroid are R and r, respectively. The coefficient of mutual induction of the toroid is ______.
(The magnetic field in it is uniform, N = number of turns, R >> r, μ0 = permeability of free space)
Write the S.I. unit of mutual inductance.
The mutual inductance of a pair of adjacent coils is 1.5 H. If the current is one coil changes from 5 A to 10 A in 0.1 s, the rate of change of magnet flux linkage is ______.
A rectangular coil of wire 50 turn each of area 6 x 10-4 m2 is freely suspended in a field of 3 x 10-2 Wb / m2. Calculate the current flowing through the coil when it deflects through 60°, when torsional constant is 3.82 x 10-6 SI unit.
State and define the SI unit of mutual inductance.
Two coils having self inductances L1 = 75 mH and L2 = 55 mH are coupled with each other. The coefficient of coupling (K) is 0. 75. Calculate the mutual inductance (M) of the two coils
