Class 12th

Two concentric circular coils, C₁ and C₂ are placed in the XY plane. C₁ has 500 turns, and a radius of 1 cm. C₂ has 200 turns and radius of 20 cm. C₂ carries a time dependent current I(t) = (5t² - 2t + 3)A where t is in s. The emf induced in C₁ (in mV ), at the instant t = 1 s is x/4. The value of x is

A particle of mass 200MeV/c² collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is N/4. The value of N is: (Given the mass of the hydrogen atom to be 1GeV/c²)

Two capacitors of capacitances C and 2C are charged to potential differences V and 2 V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives T₁(A): T₁(B): T₁(C) are in the ratio:

A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z - axis is given by:

A galvanometer of resistance G is converted into a voltmeter of range 0 - 1V by connecting a resistance R? in series with it. The additional resistance that should be connected in series with R? to increase the range of the voltmeter to 0 – 2V will b

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height h (see figure), then: (assume the remaining portion to be spherical)

For a concave lens of focal length f, the relation between object and image distances u and is v, respectively, from its pole can best be represented by ( u = v is the reference line): (Ray Optics)

With increasing biasing voltage of a photodiode, the photocurrent magnitude: