List of practice Questions

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 capacitor affected after the slab is introduced.
An electric field $\vec{E}$ 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 be few mm/s for currents in 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.
With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.
Deduce an expression for the induced emf in the coil of the 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 ?
What are coherent sources ? Why they are 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) $\frac{\lambda}{4}$ and (ii) $\frac{\lambda}{3}$.
Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power.
In a telescope the objective has much larger aperture than the eye piece. Why ?
A series combination of L, C and R is connected to an a.c. source. Using a phasor diagram, derive an expression for the impedance of the circuit and phase difference between V and I.
Under what conditions the (i) impedance of the circuit is minimum ? (ii) Wattless current flows in the circuit ?
Use Kirchhoff’s rules to find the current through $3 \Omega$ resistor in the circuit shown in the figure :
Name the electromagnetic waves which are used (iii) in water purifiers. Also write their wavelength range.
Draw electric field lines and equipotential surfaces for a system of two equal and opposite point charges separated by some distance.
Why electric field $\vec{E}$ at a point on an equipotential surface must be perpendicular to the surface at that point ?}
Consider the following nuclides : $^{12}_6\text{C}$, $^{198}_{80}\text{Hg}$, $^{14}_6\text{C}$, $^{197}_{79}\text{Au}$. Group them into isotopes and isotones.
How does the size of a nucleus depend on its mass number A ? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
Derive an expression for the magnetic field $\vec{B}$, 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.
Explain the statement : “Current is a scalar although we represent current with an arrow”.
Find ratio ($\lambda_a/\lambda_p$) of the de Broglie wavelength $\lambda_a$ and $\lambda_p$ associated respectively with an alpha particle and a proton, if they are moving with the same kinetic energy.
Find ratio ($\lambda_a/\lambda_p$) of the de Broglie wavelength $\lambda_a$ and $\lambda_p$ associated respectively with an alpha particle and a proton, just after they are accelerated through the same potential difference.
Define mutual inductance of a pair of coils. Write its SI unit.