List of practice Questions

An ac voltage $V = 280 \sin(100\pi t)$ volt is connected across a series LCR circuit in which $R = 400 \Omega$, $L = 5/\pi \text{ H}$ and $C = 50/\pi \mu\text{F}$. Taking $\sqrt{2} = 1.4$, calculate impedance of the circuit.
An ac voltage $V = 280 \sin(100\pi t)$ volt is connected across a series LCR circuit in which $R = 400 \Omega$, $L = 5/\pi \text{ H}$ and $C = 50/\pi \mu\text{F}$. Taking $\sqrt{2} = 1.4$, calculate rms value of current that flows in the circuit.
An ac voltage $V = 280 \sin(100\pi t)$ volt is connected across a series LCR circuit in which $R = 400 \Omega$, $L = 5/\pi \text{ H}$ and $C = 50/\pi \mu\text{F}$. Taking $\sqrt{2} = 1.4$, calculate power factor of the circuit.
State Lenz's law and explain that it follows the law of conservation of energy.
Write the dimensional formula for self-inductance. The current in a coil changes from 8.0 A to 2.0 A in 0.6 s. If an average emf induced in the coil is 50 V, calculate the self-inductance of the coil.
Radiation of wavelength $331\text{ nm}$ irradiates the following metals:
The ratio of amplitude of electric field to the amplitude of the magnetic field associated with an electromagnetic wave propagating in glass ($n = 1.5$) is :
Two point charges $-2\mu C$ and $5\mu C$ are placed at $(-30 \text{ cm}, 0)$ and $(30 \text{ cm}, 0)$ respectively in an external electric field $\vec{E} = \frac{A}{x^2} \hat{i}$, where $A = 9 \times 10^5 \text{ Nm}^2\text{C}^{-1}$. Find the electrostatic potential energy of this configuration.
Two infinitely long straight wires having linear charge densities $-\lambda$ and $3\lambda$ are held vertically parallel to each other, distance r apart in free space. Find the nature and magnitude of the force/length exerted by one wire on the other.
A small hollow conducting sphere of radius $r_1$ is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius $r_2$ and outer radius $r_3$, having charge $-3q$. If a point charge 2q were kept at the centre, find the electric flux through a concentric spherical Gaussian surface of radius x for (1) $x < r_1$, and (2) $r_1 < x < r_2$.
A small hollow conducting sphere of radius $r_1$ is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius $r_2$ and outer radius $r_3$, having charge $-3q$. If a point charge 2q were kept at the centre, find electric field at a point distant x from the centre for (1) $x > r_3$, and (2) $r_1 < x < r_2$.
A small hollow conducting sphere of radius $r_1$ is given a charge Q. It is surrounded by a concentric conducting spherical shell of inner radius $r_2$ and outer radius $r_3$, having charge $-3q$. If a point charge 2q were kept at the centre, find surface charge density on the inner surface of (1) sphere, and (2) shell.
A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when an iron bar is inserted inside the coil ? Justify your answer. Assume that other factors remain unchanged.
A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when the frequency of the source is decreased ? Justify your answer. Assume that other factors remain unchanged.
A point object is kept in front of a convex spherical surface of radius of curvature $R$. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance ($u$ and $v$) in terms of refractive index $n$ of the medium and $R$.
A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.
Two thin converging lenses of focal length $f_1$ and $f_2$ are placed coaxially in contact. Derive expression for the focal length of the combination.
A beam of coherent light of wavelength 550 nm is incident normal to the plane of a pair of two slits $S_1$ and $S_2$ each of width $1 \cdot 2 \times 10^{-6}$ m separated by 1.1 mm. Dark and bright fringes are observed on a screen 2.2 m away from the plane of the slits. Calculate: (I) fringe width. (II) distance of the second dark fringe from the central maximum. (III) what will happen when the entire apparatus is immersed in water.
In the figure, OA and OB show the variation of electric potential V at a point due to two point charges $Q_1$ and $Q_2$ with $1/r$ respectively. Here r represents the distance of the point from the two point charges. Identify the nature of the two charges $Q_1$ and $Q_2$.

In the figure, OA and OB show the variation of electric potential V at a point due to two point charges $Q_1$ and $Q_2$ with $1/r$ respectively. Here r represents the distance of the point from the two point charges. What is the value of $Q_1/Q_2$? Justify your answer.
An alpha particle (mass $6.4 \times 10^{-27}$ kg and charge $3.2 \times 10^{-19}$ C) having 8.0 MeV energy, enters a region of a uniform magnetic field of 0.5 T. If the field is directed perpendicular to the velocity of the particle, find the radius of the circular path described by the particle. Mention the condition under which the particle in this region (i) describes a helical path, and (ii) goes straight undeviated.
State Faraday's law of electromagnetic induction. Briefly describe two methods for producing induced emf.
A deuterium nucleus and an alpha particle approach a target nucleus separately in head-on position. Find the ratio of their distance of closest approach to the nucleus, when both have the same velocity.
A deuterium nucleus and an alpha particle approach a target nucleus separately in head-on position. Find the ratio of their distance of closest approach to the nucleus, when both have the same momentum.
Show that $\frac{1}{\sqrt{\varepsilon_0 \mu_0}}$ gives the velocity of an electromagnetic wave in free space.