CBSE EXAMINATION PAPER-2023
PHYSICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 41 questions. All questions are compulsory.
- This question paper is divided into 5 sections.
- Section A – questions number 1 to 1 are case based questions
- Section B – questions number 2 to 19 are multiple choice questions
- Section C – questions number 20 to 28 are very short answer
- Section D – questions number 29 to 35 are short answer
- Section E – questions number 36 to 41 are long answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
Diffraction of light is bending of light around the corners of an object whose size is comparable with the wavelength of light. Diffraction actually defines the limits of ray optics. This limit for optical instruments is set by the wavelength of light. An experimental arrangement is set up to observe the diffraction pattern due to a single slit.
Answer the following questions based on the above :
(1) How will the width of central maximum be affected if the wavelength of light is increased?
[1 Marks](2) Under what condition is the first minimum obtained?
[1 Marks](3) Write two points of difference between interference and diffraction patterns.
(4) Two students are separated by a 7 m partition wall in a room 10 m high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily?
Section B
An electron experiences a force (1·6 × 10¹⁶ N) î in an electric field E. The electric field E is:
To find the electric field E, we can use the formula F = qE, where F is the force experienced by the charge, q is the charge of the electron (approximately -1.6 × 10⁻¹⁹ C), and E is the electric field strength. Given the force F = 1.6 × 10¹⁶ N, we can rearrange this to find E = F/q. Plugging in the values, we get E = (1.6 × 10¹⁶ N) / (-1.6 × 10⁻¹⁹ C) = -1.0 × 10³ N/C. Therefore, the correct answer is -(1·0 × 10³ N/C) î.
The current density due to drift of electrons in a conductor is given by:
(symbols have their usual meanings)
The correct option is 'n e v_d' because current density (J) is defined as the amount of charge per unit area per unit time. Here, 'n' represents the number density of charge carriers (electrons), 'e' is the charge of an electron, and 'v_d' is the drift velocity of the electrons. Therefore, combining these factors gives the expression for current density.
Which of the following graphs correctly represents the variation of the magnitude of the magnetic field outside a straight infinite current carrying wire of radius 'a' as a function of distance 'r' from the centre of the wire?
A particle of mass m and charge q moving with a uniform velocity v = v₀ x̂ i + v₀ ŷ j enters a region with a magnetic field B = B₀ĵ. After some time, an electric field E = E₀ ĵ is also switched on in the region. The resulting path described by the particle will be:
The correct option is 'a helix with constant pitch'. Initially, the particle moves in a plane perpendicular to the magnetic field due to the Lorentz force, which will cause it to move in a circular path in the x-y plane. When the electric field is applied parallel to the magnetic field, it introduces a force in the same direction, resulting in a linear acceleration along the ĵ direction. This causes the particle to spiral upwards, maintaining a constant circular motion while translating linearly, thus forming a helix with constant pitch.
An inductor, a capacitor and a resistor are connected in series across an ac source of voltage. If the frequency of the source is decreased gradually, the reactance of :
As the frequency of the AC source decreases, the reactance of the inductor (XL = 2πfL) decreases because it is directly proportional to the frequency. Conversely, the reactance of the capacitor (XC = 1/(2πfC)) increases because it is inversely proportional to the frequency. Therefore, the correct option is that the inductor's reactance decreases and the capacitor's reactance increases.
The electromagnetic radiations used to kill germs in water purifiers are called :
The correct answer is Ultraviolet rays. Ultraviolet (UV) rays are known for their germicidal properties, and they are commonly used in water purifiers to eliminate harmful microorganisms by disrupting their DNA.
In the wave picture of light, the intensity I of light is related to the amplitude A of the wave as :
The correct option is I ∞ A². In the wave theory of light, the intensity of light is proportional to the square of the amplitude of the wave. This is because intensity is related to the energy carried by the wave, and energy is proportional to the square of the amplitude.
In a single-slit diffraction experiment, the width of the slit is halved. The width of the central maximum, in the diffraction pattern, will become :
When the width of the slit is halved, the width of the central maximum in a single-slit diffraction pattern increases. This is because the width of the central maximum is inversely proportional to the slit width. Thus, if the slit width is halved, the central maximum becomes twice as wide.
A graph is plotted between the stopping potential (on y-axis) and the frequency of incident radiation (on x-axis) for a metal. The product of the slope of the straight line obtained and the magnitude of charge on an electron is equal to :
Light of frequency 6·4 *10^14 Hz is incident on a metal of work function 2·14 eV. The maximum kinetic energy of the emitted electrons is about :
To find the maximum kinetic energy (KE) of the emitted electrons, we can use the photoelectric equation: KE = hf - W, where h is Planck's constant (4.14 x 10^-15 eV·s), f is the frequency of the light, and W is the work function. First, we calculate hf: hf = (4.14 x 10^-15 eV·s) * (6.4 x 10^14 Hz) = 2.65 eV. Then, we subtract the work function: KE = 2.65 eV - 2.14 eV = 0.51 eV. Therefore, the correct answer is 0.51 eV.
The ratio of maximum frequency and minimum frequency of light emitted in Balmer series of hydrogen spectrum, in Bohr's model is
In the Balmer series of the hydrogen spectrum, the maximum frequency corresponds to the transition from n=2 to n=infinity, and the minimum frequency corresponds to the transition from n=3 to n=2. The ratio of these frequencies can be calculated using the formula for the frequency of emitted light in the Bohr model. The correct ratio of maximum frequency to minimum frequency results in the option 9/5.
At a certain temperature in an intrinsic semiconductor, the electrons and holes concentration is 1·5*10^16 m-3. When it is doped with a trivalent dopant, hole concentration increases to 4·5 10^22 m-3. In the doped semiconductor, the concentration of electrons (ne) will be :
In a trivalent doped semiconductor, the concentration of holes (p) can be approximated by p ≈ Na (the concentration of acceptor ions). Given that the hole concentration increases to 4.5 × 10^22 m-3, we can find the electron concentration (n) using the mass action law for semiconductors, which states that n * p = ni² (where ni is the intrinsic carrier concentration, approximately 1.5 × 10^16 m-3 in this case). Thus, n = ni² / p = (1.5 × 10^16)² / (4.5 × 10^22) = 5 × 10^9 m-3. Therefore, the correct answer is 5 × 10^9 m-3.
If a p-n junction diode is reverse biased,
The correct option is 'the potential barrier is raised.' In a reverse-biased p-n junction diode, the voltage applied increases the potential barrier, making it harder for charge carriers to cross the junction. This enhances the depletion region and inhibits current flow.
A voltage signal is described by :
for a cycle. Its rms value is :
Assertion (A) : The internal resistance of a cell is constant.
Reason (R) : Ionic concentration of the electrolyte remains same during use of a cell.
Assertion (A) is false because the internal resistance of a cell is not constant; it changes with various factors like temperature and the state of charge. Reason (R) is also false since the ionic concentration of the electrolyte changes as the cell is used, affecting its performance.
Assertion (A) : When radius of a circular loop carrying a steady current is doubled, its magnetic moment becomes four times.
Reason (R): The magnetic moment of a circular loop carrying a steady current is proportional to the area of the loop.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). This is because the magnetic moment (μ) of a circular loop is given by the formula μ = I * A, where A is the area of the loop. When the radius is doubled, the area increases by a factor of four (A = πr²), thus making the magnetic moment four times greater.
Assertion (A): The nucleus 7/3 X is more stable than the nucleus 4/3 Y.
Reason (R): 7/3 X contains more number of protons.
The assertion is incorrect because a stable nucleus is not determined solely by the number of protons; it also depends on the ratio of neutrons to protons. 7/3 X being more stable than 4/3 Y is not necessarily true as the stability is influenced by other factors like neutron-proton balance.
Section C
What is meant by the term 'displacement current' ? Briefly explain how this current is different from a conduction current.
(a) State Huygens principle. How did Huygens' explain the absence of the backwave?
The refractive indices of two media A and B are 2 and √2 respectively. What is the critical angle for their interface?
(a) Draw a graph showing the variation of binding energy per nucleon as a function of mass number A. The binding energy per nucleon for heavy nuclei (A > 170) decreases with the increase in mass number. Explain.
(b) Use Huygens' principle to show reflection/ refraction of a plane wave by (i) concave mirror, and (ii) a convex lens.
(b) Using Bohr's postulates, obtain the expression for radius of nth stable orbit in a hydrogen atom.
Section D
What is meant by the term 'mutual inductance' of a pair of coils? Obtain an expression for the mutual inductance of two long coaxial solenoids, each of length l but having different number of turns N₁ and N₂ and radii r₁ and r₂ (r₂ > r₁).
An ac source v = v_m sin(ωt) is connected across an ideal capacitor. Derive the expression for the (i) current flowing in the circuit, and (ii) reactance of the capacitor. Plot a graph of current i versus ωt.
Calculate the wavelength of de Broglie waves associated with a proton having (500/1.673) eV energy. How will the wavelength be affected for an alpha particle having the same energy?
(a) (i) Prove that the nuclear density is the same for all nuclei.
(ii) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Draw two inferences from this plot.
A series combination of an inductor L, a capacitor C and a resistor R is connected across an ac source of voltage in a circuit. Obtain an expression for the average power consumed by the circuit. Find power factor for (i) purely inductive circuit, and (ii) purely resistive circuit.
(i) Draw a graph to show the variation of the number of scattered particles detected (N) in Geiger-Marsden experiment as a function of scattering angle (θ).
(ii) Discuss briefly two conclusions that can be drawn from this graph and how they lead to the discovery of the nucleus in an atom.
Section E
(a) (i) Define electric flux and write its SI unit.
(ii) Use Gauss' law to obtain the expression for electric field due to a uniformly charged infinite plane sheet.
(iii) A cube of side L is kept in space, as shown in the figure. An electric field E = (Ax + B) i N/C exists in the region. Find the net charge enclosed by the cube.
(a) (i) Write the principle and explain the working of a moving coil galvanometer. A galvanometer as such cannot be used to measure the current in a circuit.
(ii) Why is the magnetic field made radial in a moving coil galvanometer? How is it achieved?
(a) (i) Draw a ray diagram showing the formation of a real image of an object placed at a distance 'u' in front of a concave mirror of radius of curvature 'R'. Hence, obtain the relation for the image distance 'v' in terms of u and R.
(ii) A 1.8 m tall person stands in front of a convex lens of focal length 1 m, at a distance of 5 m. Find the position and height of the image formed.
(b) (i) Define electric potential at a point and write its SI unit.
(ii) Two capacitors are connected in series. Derive an expression of the equivalent capacitance of the combination.
(iii) Two point charges +q and -q are located at points (3a, 0) and (0, 4a) respectively in x-y plane. A third charge Q is kept at the origin. Find the value of Q, in terms of q and a, so that the electrostatic potential energy of the system is zero.
(b) (i) Derive an expression for magnetic field on the axis of a current carrying circular loop.
(ii) Write any two points of difference between a diamagnetic and a paramagnetic substance.
(b) (i) Draw a ray diagram showing refraction of a ray of light through a triangular glass prism. Hence, obtain the relation for the refractive index (μ) in terms of angle of prism (A) and angle of minimum deviation (δm).
(ii) The radii of curvature of the two surfaces of a concave lens are 20 cm each. Find the refractive index of the material of the lens if its power is -5·0 D.
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