## Physics midterm, for class XII

SUB: PHYSICS

TIME: 3.15 Hrs                                                                                            MAXIMUM MARKS: 90

GENERAL INSTRUCTIONS:

1.    Draw relevant diagram, figure wherever necessary.

2.    Numerical problems should be solved with the relevant formulas.

### PART — A

I. Answer all the following questions, 1 mark each ( 1 × 10 = 10 )

#### Question 1

Which of the following drops faster?

A. An electric dipole’s electric field                      B. An electric dipole’s electric potential

C. A point charge’s electric field                            D. A point charge’s electric potential

#### Question 2

Which medium will have a stronger electrostatic force between 2 charges?

A. Medium with $\epsilon = 10$                       B. Medium with $\epsilon = 100$

C. Medium with $\epsilon = 81$                      D. Free space, $\epsilon = \epsilon_0$

#### Question 3

Pick only the correct one “between an $\alpha-{particle}$ and a proton”

A. The $\alpha-{particle}$ has more specific charge.

B. The proton has more specific charge.

C. The $\alpha-{particle}$ has more specific charge if its immersed in a medium with permittivity $\epsilon_0 = 81$ than in free space.

D. The proton has more specific charge if its immersed in a medium with permittivity $\epsilon_0 = 81$ than in free space.

#### Question 4

Chose the correct one

A. Kirchhoff’s loop rule is applied to a junction of incoming and outgoing current?

B. According to Kirchhoff’s loop rule a junction of incoming and outgoing current carries a potential proportional to the amount of current flowing through the junction.

C. Kirchhoff’s junction rule can be applied to a single current carrying path in any electric circuit.

D. The potential drop in a loop in any electric circuit is zero and its based on conservation of energy.

#### Question 5

Chose the correct one

A. Resultant of capacitance in series is more than individual resistances

B. Current division works on the basis of direct proportionality of resistances

C. Voltage division works on the basis of direct proportionality of resistances

D. Resistors in series will add up

#### Question 6

Ohms’ law corresponds to the following

A. Voltage and current are proportional even if resistance varies.

B. Conductivity is the ratio of current density and electric field.

C. Resistances must add up in parallel combination.

D. Linear relation between voltage and current can be accommodated to an arbitrary range of resistances.

#### Question 7

If we define a system-of-unit where permittivity of free space is 1 and electric field intensity E value is 1, which is the correct value for energy density?

A. $\frac{1}{2}$                        B. $\frac{1}{3}$

C. 2                                D. 3

#### Question 8

If we define a system-of-unit where capacitance of a configuration is 1 and potential difference of the same Is 1 what is the electrostatic energy of the capacitor?

A. $\frac{1}{2}$                           B. $\frac{1}{3}$

C. 2                                D. 3

#### Question 9

If $10$ electrons passing through an unit cross section area A constitute a current of $10 \times 1.6 \times 10^{-19}\,\frac{C}{s}$ flowing across it, whats the drift velocity of the electrons?

A. 1 unit                B. 2 units                 C. 0.5 units                D. 5 units

#### Question 10

A capacitor of $16 \,\mu F$ is filled with dielectric of dielectric strength $K = 5$ — or permittivity $\epsilon$. Whats the new value of capacitance given a potential difference $V = 1000 \,volt$ is found on the capacitor.

A. $80 \,\mu F$                                             B. $\frac{16}{5} \,\mu F$

C. $\frac{5}{16} \,\mu F$                                           D. indeterminate

### PART — B

II. Answer all of the following 10 questions, 2 marks each. (2 × 10 = 20)

#### Question 1

Define “Temperature coefficient of resistance” $\alpha$ of a metal.

#### Question 2

Describe de-Broglie wavelength in 1 or 2 lines and write the formula that we use for this idea.

#### Question 3

Define Bohr radius of hydrogen atom; $a_0$, and state its value in pico-meter.

#### Question 4

Given Bohr radius of hydrogen atom; $a_0$, what would be the radius of the $5^{th}$ excited orbit $(n = 6)$.

#### Question 5

Whats the speed of an electron in a hydrogen atom in terms of speed of light c, if its revolving in the $7^{th}$ orbit; $v_n = v_7$, according to the Bohr’s model of an atom?

#### Question 6

Give example of 3 conservative forces. A conservative force is defined through the following; “The work done in a conservative force field during a circular voyage is zero, as such work done are independent of the path taken”.

#### Question 7

Write out the expression of $n-th$ level atomic spectra (energy level) of a hydrogen atom. What energy will be released if the electron jumps from $5^{th} \to 2^{nd}$ level?

#### Question 8

Whats the power of a lens whose object distance is $10\,cm$ and whose image distance is $50 \,cm$?

#### Question 9

Whats the focal length of a convex lens if the object distance is $15\,cm$ and image distance is $20 \,cm$.

#### Question 10

Whats the resistance of a wire that obeys Ohm’s law if it carries a current of $2 \,amp$ when a potential difference of $230 \,volt$ is applied across its ends?

### PART — C

This question is compulsory. (5 × 1 = 5)

#### Question 1

Define electric current and electric current density. State and explain Ohm’s law. Derive an expression for drift velocity.

Answer any six from Question 2 – 8. (5 × 6 = 30)

#### Question 2

Derive the electric field vector $\vec{E}$for the dipole vector $\vec{P}$, $\vec{E}_{||}$; in a direction of alignment with the dipole vector, also called End-On configuration. Show that the electric field due to a dipole vector is zero along a line perpendicular to it.

#### Question 3

Derive the magnetic field due to a solenoid by using Ampere’s circuital law.

#### Question 4

Define electric flux $\Phi_E$ and write out expression for it for a uniform and non-uniform electric field E. State and explain Gauss law in terms of charge and flux. Apply the Gauss law to the case of an infinitely straight distribution of charge with linear density of charge $\lambda$.

#### Question 5

Derive the expression for combination of 3 capacitors in series. Whats the capacitance of a combination of two capacitors each with capacitance $5\,\mu F$ connected in series. Whats the value if these are connected in parallel. Derive the energy associated with a capacitor.

#### Question 6

Derive the expression for the capacitance of a configuration where two plates are kept distance $d$ apart when a material of thickness $t$ with dielectric constant $K$ is inserted in-between.

#### Question 7

Derive the magnetic field B of a toroid by using Ampere’s circuital law.

#### Question 8

State the Ampere circuital law and define magnetic flux. State the right hand thumb rule for magnetic field created by electric current. From the Lorentz Force expression derive the force acting on a current element of length $l$ by a magnetic field $B$.

This question is Compulsory. (5 × 1= 5)

#### Question 9

Describe the mechanism of an X-ray tube. Is X-ray deflected by electric or magnetic field? Explain why.

Each carries 5 marks, answer only two from Questions 10 – 12. (5 × 2= 10)

#### Question 10

Describe the Bohr model for atom and point out its drawbacks. Write the $n^{th}$ level energy of a hydrogen atom. Calculate the emission energy of a hydrogen atom if an electron jumps from $n = 6 \to n = 5$level.

#### Question 11

Describe the Thomson’s $\frac{e}{m}$ experiment by mutually perpendicular set-up of electric field and magnetic field; E and B. Derive in necessary steps how $\frac{e}{m}$ would be determined by this set up from various known parameters such as E and B values.

#### Question 12

Threshold wavelength of Tungsten is $2400 \,A^0$. Tungsten is illuminated by a light of wavelength $1600 \,A^0$. Whats the value of work function, maximum kinetic energy of electrons and stopping potential? Describe the ideas of photoelectric effect.

### PART — D

Answer both questions. (5 × 2 = 10)

#### Question 13

State the mirror equation and thin lens formula. Derive the lens formula with a suitable diagram.

#### Question 14

Draw a simple and neat diagram showing a convex lens, optical center and focal point (focus). Now define power of a lens and obtain an expression for it. If $u = 10 \,cm$ and $v = 15 \,cm$, whats the power of the lens?