The following figure represents the electric potential as a function of x – coordinate. Plot the corresponding electric field as a function of x.

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.

The following figure shows a complex network of conductors which can be divided into two closed loops like EACE and ABCA. Apply Kirchoff’s voltage rule(KVR)

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.

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

A carbon resistor has coloured strips. What is its resistors?

Show that for a straight conductor, the magnetic field
\(\overset { \rightarrow }{ B } =\frac { { \mu }_{ ° }I }{ 4\pi a } (cos\varphi _{ 1 }-cos\varphi _{ 2 })\hat { n } \)
\(=\frac { { \mu }_{ ° }I }{ 4\pi a } (sin{ \theta }_{ 1 }+sin{ \theta }_{ 2 })\hat { n } \)

Suppose a cyclotron is operated to accelerate protons with a magnetic field of strength 1 T. Calculate the frequency in which the electric field between two Dees could be reversed.

Let I₁ and I₂ be the steady currents passing through a long horizontal wire XY and PQ respectively. The wire PQ is fixed in horizontal plane and the wire XY be is allowed to move freely in a vertical plane. Let the wire XY is in equilibrium at a height d over the parallel wire PQ as shown in figure.

Show that if the wire XY is slightly displaced and released, it executes Simple Harmonic Motion (SHM). Also, compute the time period of oscillations.

The current in an inductive circuit is given by 0.3 sin (200t – 40°) A. Write the equation for the voltage across it if the inductance is 40 mH.

Using Lenz’s law, predict the direction of induced current in conducting rings 1 and 2 when current in the wire is steadily decreasing.

The magnetic flux through a coil perpendicular to the plane is given by Φ = 5t³ +4t² +2t calculate the induced emf through the coil at t = 2S

A pulse of light of duration 10⁻⁶ s is absorbed completely by a small object initially at rest. If the power of the pulse is 60\(\times\) 10⁻³ W. Calculate the final momentum of the object.

A parallel plate capacitor is charged by an external ac source straight the displacement current inside the capacitor is the same as the current charging the capacitor.

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?

A consider the situation in the figure. The bottom of the pot is a reflecting plane mirror. F is a fish and B is a bird. (a) At what distance(s) from itself will the fish see the image (b) At what distance(s) from itself will the bird see the image(s) of the fish? Take \(\\ { m }_{ wa }=\cfrac { 4 }{ 3 }\).

X -rays of wavelength 'A' fallon a photosensitive surface emitting electrons. Assuming that the work function of the surface can be neglected, prove that the de Broglie wavelength of electrons emitted will be \(\sqrt { \frac { h\lambda }{ 2mc } } \)

Consider the case of bombardment of ²³⁵U nucleus with a thermal neutron. The fission products are ⁹⁵Mo and ¹³⁹La and two neutrons. Calculate the energy released. (Rest masses of the nuclides: ²³⁵U = 235.0439 u, \(_{ 0 }^{ 1 }{ n }\) = 1.0087 u, ⁹⁵Mo = 94.9058 u, ¹³⁹La = 138.9061 u, Take 1 u = 931 MeV.)

In the circuit shown in the figure, the BJT has a current gain (β) of 50. For an emitter-base voltage V_EB = 600 mV, calculate the emitter-collector voltage V_EC (in volts).

Write the advantages and disadvantages of robotic.