# Optionals IAS Mains Physics: Questions 86 - 92 of 306

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## Question 86

Appeared in Year: *2015*

### Write in Short

Short Answer▾Show that the rest mass energy of an electron is (10 Marks)

## Question 87

Appeared in Year: *2002*

### Describe in Detail

Essay▾A series LCR circuit with is powered by a source of volts and variable frequency. Find (a) resonant frequency (20 marks)

### Explanation

The resonance frequency is given by

(b) The Quality factor of the circuit - >

The Q is given by

(c) The width of resonance is - >

(d) The maximum content at resonance.

At resonance Impedance in the circuit = resistance R

Amplitude or peek value of the curents=

## Question 88

Appeared in Year: *2003*

### Describe in Detail

Essay▾In the following circuit, show that the stability factor S is given by

Where

(20 Marks)

### Explanation

It is desirable and necessary to keep constant in the face of variations of (sometimes represents as). The extent to which a biasing circuit is successful in achieving this goal is measured by stability factor S. It is defined as the rate of change of collector current w. r. t. the collector leakage current at content and is called stability

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## Question 89

Appeared in Year: *2007*

### Describe in Detail

Essay▾Obtain the solution of the Laplace equation in cylindrical coordinates. (20 Marks)

### Explanation

- The Laplace equation for the potential V is ……………eq. (1)
- In cylindrical coordinates Laplace equation is written in the from …………. . eq. (2)
- From equation (2) it is obvious that the potential function V is a function, hence using the method of separation of variable, we may write …………. eq. (3)
- Substituting this in equation (2), we get
- Dividing above

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## Question 90

Appeared in Year: *1999*

### Describe in Detail

Essay▾What is Meissner’s effect? Superconducting tip has a critical temperature of in zero magnetic field and critical field at gauss. Determine the critical field at.

### Explanation

- Perfect diamagnetism effect: Meissner and Ochsenfeld discovered in that a superconductor expelled the magnetic flux as the former was cooled below in an external magnetic field i. e. it behaved as a perfect diamagnet. This phenomenon is known as the Meissner effect. Such a flux exclusion is also observed if the superconductor is first cooled below

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## Question 91

Appeared in Year: *2009*

### Describe in Detail

Essay▾Derive an expression for the specific heat of a solid on the basis of Debye’s model. Show that it converges to Dulong and Petit’s law at high temperature. (25 Marks)

### Explanation

- The Debye Approximation: - If the interatomic distance is small as compared to the wavelength of elastic waves, the crystal can be regarded as a continuum from the point of view of the wave. Based on this idea, Debye assumed that the continuum model is applicable to all possible vibrational modes of the crystal. Further, the fact that the crystal c

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## Question 92

Appeared in Year: *2002*

### Describe in Detail

Essay▾Show that for a cubic lattice the difference between the successive planes is given by (10 marks)

### Explanation

- Consider a set of parallel planes with indices. Take origin on a lattice point of one such plane and draw crystallographic axes a, b and c. Now consider anther similar plane adjacent to this plane.
- Since the second plane also has the same Miller indices the lengths of the intercepts on a, b & c are respectively. If we draw a normal from the origin

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