List of practice Questions

Under what conditions the
• [(i)] impedance of the circuit is minimum?
• [(ii)] wattless current flows in the circuit?

With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

If T is the time period of the rotation of the coil, at what values of T in a cycle, the emf generator is maximum ?

Deduce an expression for the induced emf in the coil of the generator.

Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive the expression for its magnifying power.

In a telescope the objective has much larger aperture than the eyepiece. Why?

Write two advantages of reflecting telescope over refracting telescope.

Derive an expression for the capacitance of a parallel plate capacitor of plate area \(A\) and plate separation \(d\) with air present between the plates.

Two air-filled capacitors of capacitances \(C_1\) and \(C_2\) are connected in parallel with a dc battery. After the capacitors are fully charged, a slab of dielectric constant \(K\) is inserted between the plates of each capacitor. How will the
• [(i)] charge on each capacitor, and
• [(ii)] energy stored in the capacitors be affected after the slab is introduced?

An electric field \(E\) is established across the ends of a cylindrical conductor of length \(L\) and area of cross-section \(A\). Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this ‘average velocity’ of electrons.

This ‘average velocity’ is found to be only a few mm/s for currents in the range of a few amperes. How then is current established almost the instant a circuit is closed?

Two copper wires having their radii in the ratio of \(3:2\) are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

What are coherent sources? Why are they necessary for observing stable interference pattern? Draw a graph showing the variation of intensity of light with the position on the screen in Young’s double-slit experiment.

Find the intensity of light at a point on the screen when two interfering waves of the same intensity \((I_0)\) have a path difference of
(i) \(\frac{\lambda}{4}\)
(ii) \(\frac{\lambda}{3}\)

Use Kirchhoff’s rules to find the current through \(3\,\Omega\) resistor in the circuit shown in the figure.

Derive an expression for the magnetic field \(B\), due to a circular coil of \(N\) turns, each of radius \(r\) carrying current \(I\), at a distance \(x\) from the centre along its axis.

Two point charges \(-q\) and \(+q\) are located at points \((-a, 0, 0)\) and \((a, 0, 0)\) respectively. Find the electrostatic potential at point \((x, 0, 0)\) where \(x \gg a\).

Name the electromagnetic waves which are used for (i) detection of fractures in bones
(ii) physiotherapy
(iii) radar systems
Also write their wavelength range.

Define mutual inductance of a pair of coils. Write its SI unit.

A long solenoid of radius \(R\) and length \(L\) has \(n\) turns per unit length. A circular loop of radius \(r(<R)\) is placed inside at the centre of the solenoid such that its axis coincides with the axis of the solenoid. Obtain the mutual inductance of the solenoid and the loop.

Two long straight parallel conductors A and B carrying steady currents \(I_a\) and \(I_b\) in the same direction are separated by a distance \(d\). Deduce the expressions for the force acting on length \(L\) of conductor B due to conductor A and show it in figure. Write the expression for the force acting on length \(L\) of conductor A due to conductor B and show that it follows Newton’s third law.

State Bohr’s second postulate and mention its significance.

Prove that, in Bohr model of hydrogen atom as principal quantum number \(n\) becomes large, the energy levels get closer and closer.

Explain the statement: “Current is a scalar although we represent current with an arrow”.

Find ratio \( \left(\frac{\lambda_a}{\lambda_p}\right) \) of the de Broglie wavelength \( \lambda_a \) and \( \lambda_p \) associated respectively with an alpha particle and a proton,
(i) if they are moving with the same kinetic energy.
(ii) just after they are accelerated through the same potential difference.