PYQ Bank

What value of inductance has to be used so that a lamp with rating of 200 volt and 10 Amperes lights the same way with 250 V source at 50 Hz.

A conducting sphere of radius `a' is placed in a uniform electric field E_0. Using the method of images, show that the potential function is given by \phi = -E_0 \left(r - \frac{a^3}{r^2}\right) \cos \theta.

An inductance is connected to 6 volt battery through a resistance R. What is the steady state current in the circuit? Alter what time the battery would be delivering one half its steady state current?

Explain the use of a parallel resonance circuit

(i) as a rejector circuit

(ii) for current amplification.

Derive the energy continuity equation for electromagnetic waves using the poynting vector.

Find the power dissipated by R and power stored in L.

At what time are these voltage drops equal?

Current is flowing in a single-turn circular coil of radius 0.1\text{ m} such that at a point 5\text{ mm} from the centre of the coil on the axis perpendicular to the plane of the coil the magnetic field is 0.1\text{ mT}. Find the current in the coil. Hence calculate the magnetic moment of the current carrying coil.

A series R-L circuit has a constant d.c. voltage V applied at the time t = 0 by closing a switch. Derive an expression for the current in the circuit.

The introduction of the displacement current is one of the major contributions of Maxwell. Discuss.

Using Maxwell's equations, derive the electromagnetic wave equations for a conducting medium and solve it.

What is the limiting case of a metallic conductor in the above case ? Explain

For an R-L- C series resonant circuit, show that f_0 = \sqrt{f_1 f_2}, where f_0 is the resonance frequency and f_1, and f_2 are the half-power frequencies. Is this relation true for a parallel resonance circuit in which R, L and C are connected in parallel to each other? Explain.

Calculate the voltage drops across R and across L.

Show that the steady -state energy is stored in the magnetic field.

Two inductance coils hang inductances L_1 and L_2 and negligible resistances are connected in parallel. The coils have a mutual inductance M. Obtain an expression for the effective inductance of the combination.

In the given circuit the output voltage v_0 at time t second after closing the key K is 1 volt. Calculate the rate of change of current in the inductance coil at this moment.

A potential field is given by: \phi = (x^2 + y^2 + z^2)\text{ volt.} Find the electric field at a point (x, y, z) and the charge density in the region.

In a series L–C–R circuit connected to an alternating constant voltage source the current amplitude is (1/n) times the amplitude at resonance at frequencies w_1 and w_2. Obtain an expression for its quality factor at resonant frequency.

An L–C–R circuit has a resistance of 100 ohms, a capacitance of 0.2 \mu\text{F} and an inductance of 5 H. An ac source E = 50 \sin (1000 t)\text{ volt} is connected in the circuit. Calculate the average power dissipated.