A water molecule has an electric dipole moment of 6.3 x 10^-30 Cm. A sample contains 10²² water molecules, with all the dipole moments aligned parallel to the external electric field of magnitude 3 x 10⁵ NC^-1. How much work is required to rotate all the water molecules from θ = 0° to 90°? 

A parallel plate capacitor filled with mica having ε_r = 5 is connected to a 10 V battery. The area of the parallel plate is 6 cm² and separation distance is 6 mm.
(a) Find the capacitance and stored charge.
(b) After the capacitor is fully charged, the battery is disconnected and the dielectric is removed carefully.
Calculate the new values of capacitance, stored energy and charge.

For the given capacitor configuration
(a) Find the charges on each capacitor
(b) potential difference across them
(c) energy stored in each capacitor

A battery has an emf of 12 V and connected to a resistor of 3 Ω. The current in the circuit is 3.93 A. Calculate
(a) terminal voltage and the internal resistance of the battery
(b) power delivered by the battery and power delivered to the resistor

In a Wheatstone’s bridge P = 100 Ω, Q = 1000 Ω and R = 40 Ω. If the galvanometer shows zero deflection, determine the value of S.

Find the heat energy produced in a resistance of 10 Ω when 5 A current flows through it for 5 minutes.

The current through an element is shown in the figure. Determine the total charge that pass through the element at a) t = 0 s, b) t = 2 s, c) t = 5s

Two cells each of 5V are connected in series with a 8 Ω resistor and three parallel resistors of 4 Ω, 6 Ω, and 12 Ω. Draw a circuit diagram for the above arrangement. Calculate
(i) the current drawn from the cells
(ii) current through each resistor

An electron moving perpendicular to a uniform magnetic field 0.500 T undergoes circular motion of radius 2.50 mm. What is the speed of electron?

A conductor of linear mass density 0.2 g m^–1 suspended by two flexible wire as shown in figure. Suppose the tension in the supporting wires is zero when it is kept inside the magnetic field of 1 T whose direction is into the page. Compute the current inside the conductor and also the direction of the current. Assume g = 10 m s^–2

An inverter is common electrical device which we use in our homes. When there is no power in our house, inverter gives AC power to run a few electronic appliances like fan or light. An inverter has inbuilt step-up transformer which converts 12 V AC to 240 V AC. The primary coil has 100 turns and the inverter delivers 50 mA to the external circuit. Find the number of turns in the secondary and the primary current.

A rectangular coil of area 6 cm² having 3500 turns is kept in a uniform magnetic field of 0.4 T. Initially, the plane of the coil is perpendicular to the field and is then rotated through an angle of 180^o . If the resistance of the coil is 35 Ω, find the amount of charge flowing through the coil.

Calculate the instantaneous value at 60^o, average value and RMS value of an alternating current whose peak value is 20 A.

A magnetron in a microwave oven emits electromagnetic waves (em waves) with frequency f = 2450 MHz. What magnetic field strength is required for electrons to move in circular paths with this frequency?

A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. What is the distance between the first dark fringes on either side of the central bright fringe?

Lights of two wavelengths 560 nm and 420 nm are used in Young’s double slit experiment. Find the least distance from the central fringe where the bright fringes of the two wavelengths coincide. Given D = 1 m and d = 3 mm.

A monochromatic light of wavelength of 500 nm strikes a grating and produces fourth order maximum at an angle of 30°. Find the number of slits per centimeter.

A small telescope has an objective lens of focal length 125 cm and an eyepiece of focal length 2 cm.
(a) What is the magnification of the telescope?
(b) What is the separation between the objective and the eyepiece?
(c) What is the angular separation between two stars when viewed through this telescope if they subtend 1' for bare eye?

How many photons of frequency 10¹⁴ Hz will make up 19.86 J of energy?

Calculate the de Broglie wavelength of a proton whose kinetic energy is equal to 81.9 x 10^–15 J. (Given: mass of proton is 1836 times that of electron).

Calculate the radius of the earth if the density of the earth is equal to the density of the nucleus.[mass of earth 5.97 x 10²⁴ kg].

Compute the binding energy of  \(_{ 2 }^{ 4 }{ He }\) nucleus using the following data: Atomic mass of Helium atom M_A(He) = 4.00260u and that of hydrogen atom, m_H = 1.00785u.

Calculate the range of the variable capacitor that is to be used in a tuned-collector oscillator which has a fixed inductance of 150 μH. The frequency band is from 500 kHz to 1500 kHz.