HSC NOTES FOR TEACHING AND LEARNING

 

HSC PHYSICS NOTES

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Study material for July 2024Suplimetry HSC BOARD EXAM

 Study material

 for July 2024 

Suplimetry HSC BOARD EXAM

For all subjects

https://maa.ac.in/index.php?tcf=examcontent12

Study of Logarithmic Table and other Tables

Visit: www.ravindrawaykolesciphy.blogspot.com 

For 11th and 12th Students

 USE OF LOGARITHMIC TABLES & OTHER MATHEMATICAL TABLES

In Physics practicals and numerical problems we are required to use the logarithmic tables for calculations. 

The logarithmic tables are used for multiplications, divisions, squaring and finding the roots of the numbers. Logarithm of a number consists of the following two parts:

(i) Characteristics (C):- Integral part 

(ii) Mantissa:- Decimal part.

logarithm of a number = Characteristic + Mantissa

For example : log 49 = 1.6902 

In the answer before decimal number 1 is the Characteristics and .6902 is mantissa.

(A) Determination of the Characteristics:–

(i) Characteristics for numbers  greater than or equal to 1:

 The Characteristics of such number is positive.

Rule: Count the number of digits (d) in the integral part of the given number, subtract 1 from it and you will get the characteristics (C). 

i.e. C = (d-1). 

Some examples:

(ii) Characteristics of a number less than 1:

Such numbers have only decimal part. The characteristics of such number is negative.

Rule: Count the number of zeros (z) immediately following the decimal part; add 1 to it and you will get the characteristics i.e. C and is read as bar C.

Examples:-

(B) Determination of Mantissa: 

Rule: To find the mantissa, first convert the given number in four figure number by approximation. For example: 273.16 ⇒ 273.2

Divide given four figure number into three groups as: 

Refer the logarithmic table and search two digit number i.e. 27 given in the first box in the first column the of the Logarithmic table. 

Consider the row with the number 27. In this row, the number under the column headed by Third digit i.e. 3 is 4362. 

 In the same row, the number in the Mean Difference column headed by 2 is 3. 

 Add this number 3 to 4362 gives 4365. The mantissa for the logarithm of the given number is 0.4366. The characteristics of the number 273.2 is 2. 

 Therefore the

 log 273.2 = 2 + 0.4365 = 2.4365

Part –B: Antilogarithm (Abbreviation: Antilog)

It is the reverse process of logarithm that is you are given the logarithm of a number in the form ⇒ 

log N = Characteristics + Mantissa

 i.e. log 273.2 = 2.4365

From 2.4365, we have to find original number N (i.e. 273.2).

∴ Antilog (log N) = N

 Rule: Consider the four figure mantissa part in the decimal part (with the decimal point) of 2.4365 (i.e. .4365)

Now refer the Antilogarithmc Table, use the same method as you use for finding the logarithm.

Now add add number 3 to 2729 gives as 2729+3 = 2732

Use the following rules, to find the number of digits in the integral part of the number. i.e. Position of Decimal point in the final answer.

RULES: (1) If the characteristic is zero the number of digit in the integral part of the number is one.

 (2) If the characteristic is positive, the number of digits in the integral part of the number is one more than the characteristics. (i.e. C + 1). 

(3) if the characteristic is negative the number of zeros following the decimal point 

( before the first significant figure) is one less than the numeral value of the characteristics.

For Example: If the characteristic is 2, put the decimal point after first three digits. If the characteristic is bar 3, write two zeros between decimal point and first digit. 

 ∴ Antilog (2.4365) = 273.2 OR 2.732 × 10²                                                                    

LOG AND ANTILOG OF SOME NUMBERS

Laws (Theorems)of Logarithms 

PART:C 

Use of Reciprocal Table

Take the first for digits of one digit- integer number. Find the first two digit number with decimal point between in the first column of the reciprocal table. Follow the same procedure as for logarithm of number, but the number from the main difference column has to be subtracted.

For Example: Reciprocal of 3.372 = 1/ 3.372, find 3.3 in the first column; proceed along in row to the column headed 7 the figure there is 2967 then we proceed along the same row to the mean difference part and find the figure in the column headed 2.

 It is 2.  Subtract it from 2967 and we get 2965.

∴ 1/ 3.372 = 0.2965

Rules: 1) Reciprocal of a number more than one:

 Experess the given number in the form of First two digit number with decimal point between multiplied by a factor of appropriate + ve power of 10 and find the reciprocal. 

Example: 1/751.6 = 1/ 7.516× 10² = 0.1331 × 10-³ = 0.001331

2)  Reciprocal of a number less than 1:

Experess the given number in the form of First two digit number with decimal point between multiplied by a factor of appropriate - ve power of 10 and find the reciprocal. 

Example: 1/ 0.03216= 1/ 3.216× 10-² = 0.3109× 10² = 31.09

EXERCISE-2:

Find the reciprocals of :     

(i) 73.5  (ii) 591.1  (iii) 0.4216    (iv) 0.08192    (v) 0.003572 

EXERCISE-3 

Use Trigonometric Tables, Natural Sines, Natural Cosines Natural Tangents Tables. 

Note: The method of using the table is similar to that for logarithm of a number.                                                                      

For sine & tangent table, add the mean difference but for cosine table subtract the mean difference. 

1) Find sin θ  for following the angles :

     (a) 30⁰ (b) 60⁰ 36' (c) 24⁰ 15' 

2) Find cos θ for following the angles : 

     (a) 40⁰ (b) 54⁰ 12' (c) 23⁰ 25' 

3) Find tan θ for following the angles : 

     (a) 45⁰ (b) 39⁰ 24' (c) 50⁰ 7' 

EXERCISE-4  Inverse of trigonometric values: 

Find the angle θ  in the following cases: 

 (i)  sin θ =   0.1739                         (ii) cos θ = 0.9390       

 (iii) tan θ = 1.2550 

## ANSWERS:  

EXERCISE-1 

1) 3526     2) 15.81  3) 67.08        

4) 13.81    5) 76.96  6) 25.01          7) 3.004    8) 0.001541    

9) 12.92     10) 16.21        

11) 1.984 × 10⁶    12) 5.001×10¹²  13) 3.005          14) 5.961          

 

EXERCISE-2 

(i) 0.136 ×10 -¹ = 0.01361      

(ii)  0.1692 × 10 -² = 0.001692      (iii)  0.2378 × 10 ¹ = 2.378            (iv)  0.1221  × 10 ² = 12.21            (v) 0.2803 × 10 ³ = 280.3 

EXERCISE-3 

1) (a)  0.5000 (b)  0.8712                   (c) 0.4107 

2) (a)  0.7660 (b)  0.5850                  (c) 0.7179                                    3) (a)  1.0000   (b)  0.8214                (c) 1.1967 

EXERCISE-4 

(i)  θ = 10⁰ 1'    (ii)  θ =  20⁰ 7'        (ii) θ =  51⁰ 27 '                       

*******END*******

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        12th PHYSICS IMP  

   PRACTICE QUESTIONS 

    FOR MAHARASHTRA 

           HSC BOARD 

         CHAPTER 11 TO 16

Chapter 11. Magnetic Materials 

1. Explain the directional characteristic of a bar magnet. State its use.

2. Obtain an expression for orbital magnetic moment of an electron revolving about the nucleus of an atom. 

                   OR

Show that orbital magnetic moment of an electron revolving about the nucleus of an atom is proportional to its angular monmentum

3. State formula for gyromagnetic ratio. Find the gyromagnetic ratio of Electron. ( Given: me = 9.1 ×10⁻³¹kg, and e= 1.6 × 10⁻¹⁹ C).

4. What is the gyromagnetic ratio of an orbital electron ? State its dimensions and the SI unit.

5. State the vector form of the formula of orbital magnetic moment of an electron revolving about the nucleus of an atom. State why it is Negative? 

6. Obtain the expression for Bohr Magneton. State its value with unit.

7. Explain magnetization of a material.

8. Define magnetization. State its dimensions and the SI unit.                          OR

   Define magnetization. State its formula and SI unit.

9. Define magnetic intensity. State its dimensions and the SI unit.

10. What is the magnetic susceptibility of a medium?

11. Is magnetic susceptibility a dimensionless quantity? Why?

                *************

CHAPTERR 12.           ELECTROMAGNETIC   INDUCTION 

1) Express Faraday-Lenz’s law of electromagnetic induction in an equation form.

2) Determine the motional emf induced in a straight conductor moving in a uniform magnetic field with constant velocity.

3) Find an expression for the power expended in pulling a conducting loop out of a magnetic field.

4) What are eddy currents? State applications of eddy currents.

5) Explain and define the self inductance of a coil.

6) State and define the SI unit of self inductance. Give its dimensions.

7) Obtain an expression for the self inductance of a solenoid.

8) Derive the expression for the energy stored in the magnetic field of an inductor.

9) Obtain an expression for the self inductance of a solenoid.

10) Explain and define mutual inductance of a coil with respect to another coil.

11) Show that the mutual inductance for a pair of inductively coupled coils/circuits of self inductances L1 and L₂ is given by M = K√L1L₂ , where K is the coupling coefficient.

12) What is a transformer? State the principle of working of a transformer.

13) Describe the construction and working of a transformer with a neat labelled diagram.

14) Distinguish between a step-up and a step-down transformers.  

           *****************

      Chapter 13 AC CIRCUITS 

1) What is the average or mean value of an alternating emf? Obtain the expression for it. 

2) What is the rms value of an alternating current? Find the relation between the rms value and peak value of an alternating current that varies sinusoidaily with time.

3) What is a phasor? What is a phasor diagram ? Illustrate it with an example.

4) An alternating emf e = e₀ sin ωt is applied to a resistor of resistance R. 

Write the expression for the current through the resistor. Show the variation of emf and current with ωt. 

Draw a phasor diagram to show emf and current.

5) Draw a Phasor diagram showing e and i in the case of a purely inductive circuit.

6) An alternating emf is applied to an LR circuit. Assuming the expression for the current, obtain the expressions for the applied emf and the effective resistance of the circuit. Assume the inductor and resistor to be ideal. 

Draw the phasor diagram showing the emf and current.

7) Draw the impedance triangle for a series LCR AC circuit and write the expressions for the im-pedance and the phase difference between the emf and the current.

8) What is an acceptor circuit ? State its use.

9) Explain electrical resonance in an LC parallel circuit. Deduce the expression for the resonant frequency of the circuit.

10) What is a rejector circuit? State its use.

11) How are oscillations produced using an inductor and a capacitor?

12) Explain electrical resonance in an LCR series circuit. 

Deduce the expression for the resonant frequency of the circuit.

             **************

Chapter 14  Dual Nature of Radiation and Matter

1) With a neat diagram, describe the apparatus to study the characteristics of photoelectric effect.

2)  In the experiment to study photoelectric effect, describe the effects of the frequency and intensity of the incident radiation on the photoelectric current, for a given emitter material and potential difference across the photoelectric cell.

3) Define (1) Threshold frequency (2) Threshold wavelength (3) Stopping potential.

4) State the characteristics of photoelectric effect.

5) Define photoelectric work function of a metal.

6) Write Einstein’s photoelectric equation and explain its various tends. How does the equation explain the various features of the photoelectric effect?

7) Explain wave-particle duality of electromagnetic radiation.

8) State the de Broglie hypothesis and the de Broglie equation.

9) Derive an expression for the de Broglie wavelength associated with an electron accelerated from rest through a potential difference V. Consider the nonrelativistic case.

10) Derive an expression for the de Broglie wavelength.

            ************

Chapter 15 Structure of     Atoms and Nuclei 

1) Explain Thomson’s model of the atom. What are its drawbacks?

2) Explain Rutherford’s model of the atom. State the difficulties faced by Rutherford’s model of the atom.

3) State and explain the formula that gives wavelengths of lines in the hydrogen spectrum.

4) State the Postulates of Bohr’s atomic model.

5) speed of an electron in a Bohr orbit. Hence, show that it is inversely proportional to the principal quantum number.

6) Derive an expression for the radius of the nth Bohr orbit in an atom. Hence, show that the radius of the orbit is directly proportional to the square of the principal quantum number.

7) Show that the energy of the electron in the nth stationary orbit in the hydrogen atom is Eₙ = -RHch/n².

8) Draw a neat, labelled energy level diagram for the hydrogen atom. Hence explain the different series of spectral lines for hydrogen.

9) Obtain the ratio of the longest wavelength of spectral line in the Paschen series to the longest wavelength of spectral line in the Brackett series.

10) State the limitations of Bohr’s atomic model.

11) On the basis of the de Broglie hypothesis, obtain Bohr’s condition of quantization of angular momentum.

12) State the law of radioactive decay and express it in the exponential form.

OR 

State the law of radioactive decay. Hence derive the relation N = N₀e-λt, where the symbols have their usual meanings.

13) Define half-life a radioactive element and obtain the relation between half-life and decay constant.

14) What is meant by average life or mean life of a radioactive species ? How is it related to the half-life?

               ************

Chapter 16 Semiconductor Devices 

1)  Draw a neat block diagram of a dc power supply and state the function of each part.

                      OR 

With the help of a block diagram, explain the scheme of a power supply for obtaining dc output voltage from ac line voltage.

2) Explain full wave rectifier. State advantages of it.

3) Distinguish between a half-wave rectifier and full-wave rectifier.

4) Explain ripple in the output of a rectifier. What is ripple factor?

5) Explain the action of a capacitive filter with necessary diagrams.

6) What is a photodiode? Explain the I-V characteristics of a photodiode.

7) What is (i) dark current (ii) dark resistance of a photodiode?

8) State any  advantages and disadvantages of a photodiode.

9) State any two applications of photodiodes.

10) What is a solar cell ? State the principle of its working. State any four uses of solar cells.

11) State the material selection criteria for solar cells.

12) What is a light-emitting diode (LED)? Describe with a neat diagram the construction of an LED.

13) State any four disadvantages of an LED. State any four applications of LEDs.

14) Explain the working of an npn transistor with a neatly labelled circuit diagram.

15) Draw a neat labelled circuit diagram to study the characteristics of a transistor in common- emitter configuration.

16) What is an amplifier? Draw a neat circuit diagram of a transistor CE- amplifier and explain its working. 

17) Define the following logic gates :

(1) AND

(2) OR

(3) NOT.

Give the logic symbol, Boolean expression and truth table of each.

18) Define the logic gates (1) NAND (2) NOR.

Give the logic symbol, Boolean expression and truth table of each.

How are the above gates realized from the basic gates?

*****************************

       ALL THE BEST

IMPORTANT PRACTICE QUESTIONS 12 TH PHYSICS 

HSC MAHARASHTRA BOARD 2024

Chapter 6 to 10

Chapter 6. Superposition of Waves 

1. Equation stationary wave on stretched string and condition of nodes and antinodes ?

2. State the properties of Stationary wave.

3. Distinguish between a) progressive wave and stationary wave 

b) Free and Force vibration?

4. Obtain the expression for the frequency of the first three modes of vibration of stretched string between two rigid support with the help of neat labelled diagram. Hence show that all harmonics are present  in these vibrations.

5. Draw the neat labelled diagram of the first three modes of vibration of air column in a pipe open at one end (or closed at one end). 

Obtain the formule for the frequency of the first three modes of  vibration of air column in the same pipe. Also in this case show that odd harmonics are present. 

6. Obtain an expression for the frequency of the first three modes of vibration of air column in the pipe open at both end with neat labelled diagram. Also in this case show that even harmonics are present. 

7. Show that the fundamental frequency of vibration of the air column in a pipe open at both ends is double that of a pipe of the same length and closed at one end.

8. Two organ pipes closed at one end have the same diameters but different lengths. Show that the end correction at each end is where the symbols have their usual meanings.

9. What are beats? Define (1) the period of beats (2) beat frequency.

10. Explain the production of beats and deduce analytically the expression for beat frequency.

                    OR 

 Discuss analytically the formation of beats and show that 

(1) the beat frequency equals the difference in frequencies of two interfering waves

(2) the waxing and waning occur alternately and with the same period.

11. Explain any two applications of beats.

          ###*********###

Chapter 7. Wave Optics

1 Give a brief account of Huygens’ wave theory of light. State its merits and demerits.

2. State Huygens’ principle.

3. Explain the construction and propagation of a plane wavefront using Huygens’ principle.

4. Explain the construction and propagation of a spherical wavefront using Huygens’ principle.

5.Explain the phenomenon of polarization of light by reflection. 

                      OR 

   Explain Brewster’s law.

6. Describe with a neat labelled ray diagram the Fraunhofer diffraction pattern due to a single slit. Obtain the expressions for the positions of the intensity minima and maxima. Also obtain the expression for the width of the central maximum.

7. In Young’s double-slit experiment, a glass slide of refractive index ng and thickness b is placed in front of one of the slits. 

What happens to the interference pattern and fringe width ?

 Derive an expression for the positions of the bright fringes in the interference pattern.

8. State and explain Rayleigh’s criterion for minimum resolution.

              ###********###

PART 4

Chapter 8. Electrostatics 

1.Obtain an expression for the electric field intensity at a point outside a charged conducting spherical shell.

Hence, obtain an expression for the electric intensity 

(i) on the surface of (i.e. just outside) the spherical conductor. 

(ii) inside the spherical conductor.

2. Obtain an expression for the electric field intensity at a point outside an infinitely long charged cylindrical conductor.

3. Obtain an expression for the electric field intensity at a point outside a uniformly charged thin infinite plane sheet.

4. Obtain an expression for the electric potential energy of a system of two isolated point charges.

5. Obtain an expression for the electric potential at a point due to an isolated point charge.

6. Derive an expression for the electric potential at a point due to a short electric dipole. Hence, write the expression for the electric potential at a point 

(i) on the dipole axis 

(ii) on the dipole equator.

7. Derive an expression for the potential energy of a system of two point charges.

8. Obtain an expression for the potential energy of a configuration of N point charges.

9. Derive an expression for the electric potential energy of an electric dipole in a uniform electric field. 

                        OR

Derive an expression for the total work done in rotating an electric dipole through an angle θ in a uniform electric field.

10. Derive an expression for the effective or equivalent capacitance (capacity) of a combination of a number of capacitors connected in series.                          OR

Derive an expression for the effective capacitance of three capacitors connected in series.

11. Explain the effect of a dielectric on the capacitance of a isolated charged parallel-plate capacitor.

Hence, show that if a dielectric of relative permitivity (dielectric constant) k completely fills the space between the plates, the capacitance increases by a factor k.

12. Show that the energy of a charged capacitor is 1/2 CV². Also, express this in other forms. 

                         OR

Derive an expression for the energy stored in a charged capacitor. Express it in different forms.

              ###********###

Chapter 9. Current Elecricity

1 State Kirchhoff’s first law or current law or junction law.

2. What is the sign convention used for Kirchhoff’s first law? Explain with an example.

3. What is the sign convention used for Kirchhoff’s first law? Explain with an example.

4. What is the sign convention used for Kirchhoff’s second law ? Explain with an example.

5. Obtain the balancing condition in case of Wheatstone’s network.

6. Explain with the help of neat circuit diagram, how you determine the unknown resistance by using a meter-bridge.

7. Describe how a potentiometer is used to compare the emfs of two cells by combination method.

8. Describe with the help of a neat circuit diagram how you will determine the internal resistance of a cell by usinhg a potentiometer.

9. State the advantages of a potentiometer over a voltmeter.

10. Explain how a moving-coil galvanometer is converted into an ammeter. Derive the necessary formula.

11. Explain how a moving-coil galvanometer is converted into a voltmeter. Derive the necessary formula.

12. Distinguish between an ammeter and a voltmeter.

           ###*********####

PART 5

Chapter 10. Magnetic Fields due to Eletric Current 

1 (a) State the factors which the magnetic force on a charge depends upon and write its vector cross product relationship. 

    (b) Hence state the expression for the Lorentz force on a charge due to an electric field as well as a magnetic field.

    (c) Hence discuss the magnetic force on a charged particle which is

(i) moving parallel to the magnetic field (ii) stationary.

2. Define the SI unit of magnetic induction from Lorentz force.

3. Obtain an expression for the magnetic force acting on the straight wire carrying a current. Also extend this formula for a wire of arbitrary shape. 

4. Derive an expression for the net torque on a rectangular current-carrying loop placed in a uniform magnetic field with its rotation axis perpendicular to the field.

5. Describe the construction of a suspended-type moving-coil galvanometer with a neat labelled diagram.

6. State working of a moving- coil galvanometer (suspended-coil type).

7. State the Bio-Savart law (Laplace law) for the magnetic induction produced by a current el-ement. Express it in vector form.

8. Using Biot-Savart’s law, obtain the expression for the magnetic induction near a straight infinitely long current-carrying wire.

9. Show that currents in two long, straight, parallel wires exert forces on each other. Derive the expression for the force. 

                      OR

    Derive an expression for the force per unit length between two infinitely long parallel conductors carrying current and hence define the ampere.

10. Obtain an expression for the magnetic induction produced by a current in a wire in the shape of a circular arc at its centre of curvature. 

Hence obtain an expression for the magnetic induction at the centre of a circular coil carrying a current.

11. Derive an expression for the magnetic induction at a point on the axis of a circular coil carrying a current.

12. State and explain Ampere’s circuital law.

13. Using Ampere’s law, obtain an expression for the magnetic induction near a current-carrying straight, infinitely long wire.

14. Using Ampere’s law, derive an expression for the magnetic induction inside an ideal solenoid carrying a steady current.

15. Using Ampere’s law, derive an expression for the magnetic induction inside an ideal toroid carrying a steady current.

              ###********###