PHYSICS (Electrostatics Time Varying Fields & Electric Currents)

Optional Paper—1

Time : 3 Hours

Maximum Marks : 50

N.B. :— (1) All questions are compulsory and carry equal marks.

(2) Draw well labelled diagram wherever necessary.

**EITHER**

1. (A) State and explain Coulomb’s law in vacuum. Prove that Coulomb’s law is in accordance

with the Newton’s third law of motion. [5M]

(B) (i) Define electric potential. Show that in an electric field $Latex \overline E$ , the potential difference

between a point A and B along any path is V_{B}-V_{A }= -$Latex \int_A^B\overline E\cdot\overline{dr}$ [2M]

(ii) Calculate the potential due to a short dipole of dipole moment 3 × 10–26 c.m. at a point

at a distance of 3 cm from its centre on its axis. Given : $Latex \frac1{4\pi\varepsilon_0}$= $Latex 9\times10^9N-m^2/c^2$ [2M]

**OR**

(C) What do you mean by conservative field ? Show that electrostatic field is conservative. [2½M]

(D) Derive an expression for electric field intensity at a point due to a point charge. [2½M]

(E) Derive the relation E = –grad V. [2½M]

(F) How far should be the two protons if the electric force between them is equal to the weight

of a proton ?

Given—Mass of proton, m = 1.67 × 10^{–27} kg

Charge on proton, q = 1.6 × 10^{–19} C

$Latex \frac1{4\pi\varepsilon_0}$= $Latex 9\times10^9N-m^2/c^2$

g = 9.8 m/s^{2} [2½M]

**EITHER**

2. (A) Define Electric field intensity (E), Displacement density (D) and Polarization (P) and

derive the relation between them. [5M]

(B) (i) Explain with examples polar and non-polar dielectrics. [3M]

(ii) A parallel plate condenser is partially filled with an ebonite plate of thickness 6 mm.

If area of plates of condenser is 2 × 10–2 m2, separation between the plates is 1 cm and

dielectric constant of ebonite is 3, calculate capacity of the condenser.

[Given : $Latex \varepsilon_0$ = 8.85 × 10–12 c^{2}N^{–1}m^{–2}] [2M]

**OR**

(C) Show that capacity of a parallel plate capacitor completely filled with dielectric is given

by C=\frac{k\varepsilon_0A}d [2½M]

(D) Three parallel capacitor and three series capacitor are connected in parallel. If the capacity

of each capacitor is ‘C’, find the capacitance of their combination. [2½M]

(E) Discuss different types of polarizability in dielectrics. [2½M]

(F) If the capacity of condenser changes from 1000 μF to 1500 μF when the dielectric is

introduced. Find out the value of dielectric constant introduced. [2½M]

**EITHER**

3. (A) Describe the construction and theory of transformer with neat labelled diagram. [5M]

(B) (i) What are the different types of losses associated with the transformer ? How can they

be minimize ? [3M]

(ii) A transformer is used to glow a 140 W – 240 V bulb at 240 V a.c. If current in the

primary coil is 0.7 A, calculate the efficiency of the transformer. [2M]

**OR**

(C) Derive equation of continuity for time varying currents. [2½M]

(D) Derive an expression for decay of charge in CR circuit. [2½M]

(E) State and explain Kirchoff’s current and Voltage law. [2½M]

(F) In an LR circuit, the current attains 1/3rd of its final steady value in 5 sec. What is the time

constant of the circuit ? [2½M]

**EITHER**

4. (A) Explain the term impedance and reactance. Obtain an expression for the power consumed

in an ac circuit ? What is Wattless current ? [5M]

(B) (i) What is Q-value of series LCR circuit ? How it signify the sharpness of resonance ?

On what factor does it depends ? [3M]

(ii) Find out the resonance frequency of series LCR circuit for L = 100 μH, R = 5 W and

C = 0.002 μF. [2M]

**OR**

(C) Show that in a pure inductive circuit, the current lags behind the applied emf by 90º. [2½M]

(D) An electric lamp marked 100 Volts d.c. consumes a current of 10 A. It is connected to a

200 Volts, 50 cycles a.c. mains. Calculate the inductance of the required choke. [2½M]

(E) By j-operator method, obtain an expression for the current in an ac circuit containing

capacitance and resistance. [2½M]

(F) How a.c. current and voltages are expressed in complex number form ? Explain. [2½M]

5. Attempt any TEN : [10M]

(i) What is electric dipole ?

(ii) State any two limitations of Coulomb’s law.

(iii) Calculate the electric field on the surface of the nucleus having atomic number 12 and

nuclear radius 2 × 10^{–10} m.

(iv) If the separation between the two plates is increased, what happens to the capacity of a

capacitor ?

(v) Define dielectric constant ‘K’.

(vi) If displacement vector, D = 26.6 × 10^{–6} c/m2, Electric field vector E = 10^{6} N/c, then

determine polarization vector P . [Given : Î0 = 8.85 × 10^{–12} C2/Nm2]

(vii) Show that time constant of CR circuit has dimension of time.

(viii) Define self inductance. State its unit.

(ix) The ratio of number of turns of primary to secondary is 1 : 20. It is connected to an A.C.

supply of 200 volts. Find the voltage across secondary of the transformer.

(x) Write the unit of reactance and impedance.

(xi) Find the reactance of capacitor of capacity 1 μF at 2 kHz frequency.

(xii) Define quality factor in terms of resonance frequency and bandwidth.

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