List of practice Questions

Plot a graph to show the variation of reactance of the element with the frequency of the applied voltage.

Name the electromagnetic radiations and write their frequency range:
(a) Used to take the photograph of the bones
(b) Produced by hot bodies
(c) Used in television communication systems

An ac source of voltage \( V = V_0 \sin \omega t \) is connected to a circuit element \( X \). It is observed that the current flowing through \( X \) varies as \( I = I_0 \sin\left(\omega t - \frac{\pi}{2}\right) \).
(a) Identify the element \( X \) and write the expression for its reactance.

Answer the following giving reasons:
(a) The maximum kinetic energy of the photoelectrons is independent of the intensity of incident radiation.
(b) Photoelectric current increases with the increase in the intensity of the incident radiation.
(c) The stopping potential \( V_0 \) varies linearly with the frequency \( \nu \) of the incident radiation for a given photosensitive surface.

Write the mathematical forms of three postulates of Bohr’s theory of the hydrogen atom. Using them, prove that for an electron revolving in the \( n^{\text{th}} \) orbit:
(a) the radius of the orbit is proportional to \( n^2 \), and
(b) the total energy of the atom is proportional to \( \left( \frac{1}{n^2} \right) \).

Define the ‘distance of closest approach’. An \( \alpha \)-particle of kinetic energy \( K \) is bombarded on a thin gold foil. Derive an expression for the ‘distance of closest approach’.

(a) How are electromagnetic waves produced?
(b) Write the wavelength range and one use of:
(i) Microwaves, and
(ii) Ultraviolet waves.

The current in a solenoid decreases steadily from 6 mA to 2 mA in 50 ms. If an average emf of 0.4 V is induced, find the self-inductance of the solenoid.

Two concentric circular coils of radii \( r_1 \) and \( r_2 \) (\( r_2 \gg r_1 \)) are placed coaxially with their centres coinciding. If a current \( I \) is passed through the outer coil, obtain the expression for mutual inductance of the arrangement.

Two point charges of \( -5\,\mu C \) and \( 2\,\mu C \) are located in free space at \( (-4\,\text{cm}, 0) \) and \( (6\,\text{cm}, 0) \) respectively.
(a) Calculate the amount of work done to separate the two charges at infinite distance.
(b) If this system of charges was initially kept in an electric field \[ \vec{E} = \frac{A}{r^2}, \text{ where } A = 8 \times 10^4\, \text{N}\,\text{C}^{-1}\,\text{m}^2, \] calculate the electrostatic potential energy of the system.

In a Young’s double-slit experiment, the intensity at the central maximum in the interference pattern on the screen is \( I_0 \). Find the intensity at a point on the screen where the path difference between the interfering waves is \( \frac{\lambda}{6} \).

In the circuit shown, the charge on the left plate of the 20 µF capacitor is \( -50\,\mu C \). The charge on the right plate of the 12 µF capacitor is:

The ratio of the intensities at maxima to minima in Young’s double-slit experiment is \( 25 : 9 \). Calculate the ratio of intensities of the interfering waves.

Two wires made of the same material have the same length \( l \) but different cross-sectional areas \( A_1 \) and \( A_2 \). They are connected together with a cell of voltage \( V \). Find the ratio of the drift velocities of free electrons in the two wires when they are joined in: (i) series, and (ii) parallel.

(a) Briefly explain Einstein’s photoelectric equation.
(b) Four metals with their work functions are listed below:
K = 2.3 eV, Na = 2.75 eV, Mo = 4.17 eV, Ni = 5.15 eV.
The radiation of wavelength 330 nm from a laser source placed 1 m away, falls on these metals.
Which of these metals will not show photoelectric emission?
What will happen if the laser source is brought closer to a distance of 50 cm?

In a circular loop of radius \( R \), current \( I \) enters at point \( A \) and exits at point \( B \), as shown in the figure. The value of the magnetic field at the centre \( O \) of the loop is:

Define current sensitivity of a galvanometer. “Increasing the current sensitivity may not necessarily increase the voltage sensitivity.” Give reason.

The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focused on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)

Two coherent light waves, each of intensity \( I_0 \), superpose and produce an interference pattern on a screen. Obtain the expression for the resultant intensity at a point where the phase difference between the waves is \( \phi \). Write its maximum and minimum possible values.

(I) Write Ampere’s circuital law in mathematical form and explain the terms used.
(II) As the current-carrying solenoid is made longer, the magnetic field produced outside it approaches zero. Why?
(III) A flexible loop of irregular shape carrying current, when located in an external magnetic field, changes to a circular shape. Give reason.

A galvanometer of resistance \( G \) is converted into a voltmeter to measure up to \( V \) volts by connecting a resistance \( R_1 \) in series with the coil. If \( R_1 \) is replaced by \( R_2 \), then it can only measure up to \( \frac{V}{2} \) volts. Find the value of the resistance \( R_3 \) (in terms of \( R_1 \) and \( R_2 \)) needed to convert it into a voltmeter that can read up to 2 V.