Advertisements
Advertisements
Question
The mutual inductance between two coils is 2.5 H. If the current in one coil is changed at the rate of 1 As−1, what will be the emf induced in the other coil?
Solution
Given:-
Mutual inductance between the coils, M = 2.5 H
Rate of change of current in one coil,
`(di)/(dt)=1 "As"^-1`
The flux in the coil due do another coil carrying current i is given by
ϕ = Mi
The emf induced in the second coil due to change in the current in the first coil is given by
\[e = \frac{d\phi}{dt}\]
\[ \Rightarrow e = \frac{d(Mi)}{dt} = M\frac{di}{dt}\]
\[ \Rightarrow e = 2 . 5 \times 1 = 2 . 5 V\]
APPEARS IN
RELATED QUESTIONS
The current flowing through an inductor of self-inductance L is continuously increasing. Plot a graph showing the variation of
Induced emf versus dI/dt
Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mΩ. Assume the field to be uniform.
(a) Suppose K is open and the rod is moved with a speed of 12 cm s−1 in the direction shown. Give the polarity and magnitude of the induced emf.
(b) Is there an excess charge built up at the ends of the rods when K is open? What if K is closed?
(c) With K open and the rod moving uniformly, there is no net force on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain.
(d) What is the retarding force on the rod when K is closed?
(e) How much power is required (by an external agent) to keep the rod moving at the same speed = (12 cm s−1) when K is closed? How much power is required when K is open?
(f) How much power is dissipated as heat in the closed circuit? What is the source of this power?
(g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?
A rectangular coil of area A, having the number of turns N is rotated at 'f' revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2 πf NBA.
An aeroplane is flying horizontally from west to east with a velocity of 900 km/hour. Calculate the potential difference developed between the ends of its wings having a span of 20 m. The horizontal component of the Earth's magnetic field is 5 × 10–4 T and the angle of dip is 30°.
What is motional emf? State any two factors on which it depends.
Figure shows a conducting loop being pulled out of a magnetic field with a speed v. Which of the four plots shown in figure (b) may represent the power delivered by the pulling agent as a function of the speed v?
An LR circuit with a battery is connected at t = 0. Which of the following quantities is not zero just after the connection?
The north pole of a magnet is brought down along the axis of a horizontal circular coil (see the following figure). As a result, the flux through the coil changes from 0.35 weber to 0.85 weber in an interval of half a second. Find the average emf induced during this period. Is the induced current clockwise or anticlockwise as you look into the coil from the side of the magnet ?
The magnetic field in the cylindrical region shown in figure increases at a constant rate of 20.0 mT/s. Each side of the square loop abcd and defa has a length of 1.00 cm and a resistance of 4.00 Ω. Find the current (magnitude and sense) in the wire ad if (a) the switch S1 is closed but S2 is open, (b) S1 is open but S2 is closed, (c) both S1 and S2 are open and (d) both S1 and S2 are closed.
A closed coil having 100 turns is rotated in a uniform magnetic field B = 4.0 × 10−4 T about a diameter which is perpendicular to the field. The angular velocity of rotation is 300 revolutions per minute. The area of the coil is 25 cm2 and its resistance is 4.0 Ω. Find (a) the average emf developed in half a turn from a position where the coil is perpendicular to the magnetic field, (b) the average emf in a full turn and (c) the net charge displaced in part (a).
Figure shows a circular wheel of radius 10.0 cm whose upper half, shown dark in the figure, is made of iron and the lower half of wood. The two junctions are joined by an iron rod. A uniform magnetic field B of magnitude 2.00 × 10−4 T exists in the space above the central line as suggested by the figure. The wheel is set into pure rolling on the horizontal surface. If it takes 2.00 seconds for the iron part to come down and the wooden part to go up, find the average emf induced during this period.
A metallic metre stick moves with a velocity of 2 m s−1 in a direction perpendicular to its length and perpendicular to a uniform magnetic field of magnitude 0.2 T. Find the emf induced between the ends of the stick.
A 10 m wide spacecraft moves through the interstellar space at a speed 3 × 107 m s−1. A magnetic field B = 3 × 10−10 T exists in the space in a direction perpendicular to the plane of motion. Treating the spacecraft as a conductor, calculate the emf induced across its width.
A copper wire bent in the shape of a semicircle of radius r translates in its plane with a constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the plane of the wire. Find the emf induced between the ends of the wire if (a) the velocity is perpendicular to the diameter joining free ends, (b) the velocity is parallel to this diameter.
Consider the situation shown in figure. The wires P1Q1 and P2Q2 are made to slide on the rails with the same speed 5 cm s−1. Find the electric current in the 19 Ω resistor if (a) both the wires move towards right and (b) if P1Q1 moves towards left but P2Q2 moves towards right.
Consider the situation shown in figure. The wire PQ has a negligible resistance and is made to slide on the three rails with a constant speed of 5 cm s−1. Find the current in the 10 Ω resistor when the switch S is thrown to (a) the middle rail (b) the bottom rail.
The current in an ideal, long solenoid is varied at a uniform rate of 0.01 As−1. The solenoid has 2000 turns/m and its radius is 6.0 cm. (a) Consider a circle of radius 1.0 cm inside the solenoid with its axis coinciding with the axis of the solenoid. Write the change in the magnetic flux through this circle in 2.0 seconds. (b) Find the electric field induced at a point on the circumference of the circle. (c) Find the electric field induced at a point outside the solenoid at a distance 8.0 cm from its axis.
An inductor-coil of inductance 20 mH having resistance 10 Ω is joined to an ideal battery of emf 5.0 V. Find the rate of change of the induced emf at (a) t = 0, (b) t = 10 ms and (c) t = 1.0 s.
A small flat search coil of area 5cm2 with 140 closely wound turns is placed between the poles of a powerful magnet producing magnetic field 0.09T and then quickly removed out of the field region. Calculate:
(a) Change of magnetic flux through the coil, and
(b) emf induced in the coil.
