For an LCR circuit having resonant frequency f0 and bandwidths B1 match List I with List II and select the correct answer using the codes given below the Lists:
(A) Quality factor
(B) Band width of series resonance
(C) Impedance of a parallel resonant circuit = L/CR
(D) Time constant = L/R
An oscillating voltage V(t) = V0 sin ωt is applied across a parallel plate capacitor having a plate separation d. The displacement current density through the capacitor is
We know displacement current density
for parallel capacitor plate electric field
V → Voltage across capacitor plate
d → distance between two plate
Given V = V0 sinωt
A power (step-up) transformer with 1:8 turn ratio has 60 Hz, 120V across the primary, the load in the secondary is 104Ω. The current in the secondary is:-
An alternating potential (V) = V sin cot is applied across a circuit. As a result the current flows in it. The power consumed in the circuit per cycle is:-
(Power consumed ) P =
An ideal inductor takes current of 10 A when connected to a 125 V. 50 Hz ac supply. A pure resistor across the same source takes 12.5 A. If the two are connected in series across a 100 √2 v, 40 Hz supply, the current through the circuit will be
for resistance R=
For 40 Hz frequency
For a varying current the R.M.S. value of current will be:
A circular loop of radius a' is made of single form of thin conducting wire. The self inductance of this loop is L'. If the no. of turns in the loop is increased from 1 to 8. the self inductance would be:-
Now if n' is changed from 1 to 8
L" = 64 L
An LR circuit with a battery is connected at t = 0, which of the following quantities is/are not zero just after the connection?
Emf induced in the inductor
Which one of the following Maxwell's equations implies the absence of magnetic monopoles?
From maxwell's II equation i.e. total flux through a surface is zero which provide the absence of magnetic monopoles.
In a homogeneous non conducting region where the value of ε1 will be
Impedance Z = ...(i)
equating eq. (1) and (2)
Positive and negative point charges of equal magnitude are kept at and respectively.
The work done by the electric field when another positive point charge in moved from (-a. 0. 0) to (0. a. 0) is
For the given charge distribution the whole xy plane is an equipotential surface with potential V = 0 Hence, work done in moving a positive point charge from (- a. 0. 0) to (O.a. 0) is zero.
A certain charge Q is divided into two parts q and (Q - q). For the maximum coulomb force between them, the ratio (q/Q) is:
for F to be maximum, dF/dq =0
A charge situated at a certain distance from an electric dipole in the end on position experiences a force F. If the distance of the charge is doubled, the force acting on the charge will be:
A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin. B be the point on the x-axis at = +1 cm and c be point on the y - axis at y = +1 cm. Then the potentials at the points A. B and C satisfy:
Direction of electric field is in the direction of potential drop
A disk of radius a/4 having a uniformly distributed charge 6C is placed 8c is placed on the x- axis from x =a/4 to x = 5a/4. Two point charge - 7 c and 3c are placed at (a/4. 0) and (-3a/4,3a/4.0), respectively, consider a cubical surface formed by six surfaces x = x = ±a/2.y = ±a/2.z = ±a/2. The electric flux through this cubical surface is
Net charge enclosed by the cube
So, using gauss Law.
An electromagnetic wave whose electric field is given below
and Ey = 3E0 cos (3x + 4 y - 500t + π)
Speed v = 2 . 08 * 10-2
Direction of propagation It is perpendicular to the direction of propagation.
Polarization - Divide Ey by Ex
So this electromagnetic wave is linearly polarized with angle
Which one of the following statements are incorrect?
Magnitude of the electric field is attenuated as the wave propagates.
Two long parallel wires of zero resistance are connected to each other by a battery of 1.0 V. The separation between the wires is 0.5 m. A metal bar, which is perpendicular to the wire and of resistance 10 Ω moves on these wires when a magnetic field of 0.02 tesla is acting perpendicular to the plane containing the bar and the wires. If the mass of the bar is 0.002 kg.
Due to battery current I (= E/R)the rod in the magnetic field B will experience a force
which will accelerate the rod. However, due to motion of the rod in the field, an emf will be induced in it. Due to this induced emf, the induced current will result in a force
which will oppose the motion of the rod as shown in Fig. So the equation of motion of the rod will be
F - Fm = ma
which in the light of equation (1) and (2) reduces to
On integrating it with initial condition v = 0 at t = 0, we have
In this problem, as
This is the required result and from this it is clear that the velocity of the rod will increase exponentially with time and will reach the steady state value (called terminal velocity ) when v becomes independent of t
A conducting loop rotates with constant angular velocity about its fixed diameter in a uniform magnetic field in a direction perpendicular to that of fixed diameter
All are correct options.
i.e the emf induced is equal to change in magnetic flux per unit time.
Which of the following are correct if electrostatic potential field is given by
In charge less (free charge) medium electric field, potential satisfies aplace equation If potential does not satisfies laplace equation then it satisfies Poisson equation.
So potential does not satisfies laplace equation so. From Poisson Eq.
∴ charge density Ans.
Consider the circuit shown below. Calculate the effective resistance of the circuit and use this knowledge to find the current (in Ampere) in the 4Ω resistor.
Now working backward the I = 1 A splits first into
and then l2 splits into
A potential difference of V is applied at the ends of a copper wire of length l and diameter d. On doubling only d, drift velocity
Drift velocity is given by
Vd = V / Plane
Vd does not depend upon diameter.
Calculate the equivalent resistance between points C & D in the combination of resistance shown in figure.
Assuming that all the energy from a 2000 watt lamp is radiated uniformly, calculate the average values of the intensities of electric fields (in v/m) of radiation at a distance of 2 m from the lamp.
Let the lamp be treated as a point source.
The total flux energy over a sphere drawn round the lamp as centre - 2000 watt = 2000 J/S.
Total energy flux falling on area 4πr2?
Thus energy flux per unit area per second
EH (from poynting theorem)
Calculate the magnitude of poynting vector (in mega watt/m2) at the surface of the sun. Given that power radiated by sun is 4 * 1026 watts and radius of sun is 7 x 108m ).
Let S = Poynting vector i.e., power radiated per unit surface area of sun; R = radius of sun
∴ 4πR2 = surface area of the sun
Thus P = Power radiated by sun
= 0.00642 x 1010 = 6.42 * 107 watts/m2 = 64.2 mega watt/m2
A container of volume 1 m3 is divided into two equal parts by a partition. One part has an ideal gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be ____ .
Since . the system is insulated 0 = 0. Other part is vacuum . therefore , work done by the gas W ia also zero. Hence . from first law o f thermodynamics , ΔU = 0 i.e. temperature remains constant.
During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .
vp2 = constant
putting , we have T2/V = constant
so , if V is doubled , T becomes √2 = 1.4times.
One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is ____ .
Let four point charges and -q/2 be placed at the verticies of a square of side a. Let another point charge -q be placed at the centre of the square Let v(r) be the electrostatic potential at a point P at a distance r » a from the centre of the square. Then is_____.
A cubical box of side 1 m contains helium gas (atomic weight 4) at a pressure of 100 N/m2. During an abservation time of 1 s, an atom travelling with the root mean square speed parallel to one of the edges of the cube, was found to make 500 his with a particular wall, without any collision other atoms. Take, Evaluate the temperature of the gas.
Volume of the box = 1 m3
pressure of the gas = 100 N/m2
Let T be the temperature of the gas. Then,
Time between two consecutive collisions with one wall = 1/500s. This should to where l is the side of cube.