NEB Class 12 · Past paper
The complete NEB Class 12 2074 exam paper for Physics, all 12 questions with solved model answers.
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Answer in brief, any four questions. (a) You are given n wires, each of resistance R. What is the ratio of maximum to minimum resistance obtainable from these wires? (b) Why do we prefer a potentiometer to measure the emf of a cell rather than a voltmeter? (c) What is angle of dip? How is it related to the components of the earth's magnetic field? (d) Why is soft iron used to make the core of a transformer? (e) If the number of turns of a solenoid is doubled, keeping the other factors constant, how does the self-inductance of the solenoid change? (f) The emf of an ac source is given by E = 300 sin 314t volts. Write the values of the peak voltage and frequency of the source.
(a) The maximum resistance comes from connecting all $n$ wires in series, giving $R{max} = nR$, while the minimum comes from connecting them all in parallel, giving $R{min} = R/n$. The ratio is therefore $$ \begin{aligned} \frac{R{max}}{...
Answer in brief, any four questions. (a) Why is a neutron considered the most effective bombarding particle in a nuclear reaction? (b) The value of e/m is constant for cathode rays but not for positive rays. Why? (c) The output of a two-input AND gate is fed to a NOT gate. Give its logic symbol and write down its truth table. Identify the new logic gate formed. (d) How does a daughter nucleus differ from its parent nucleus when it emits (i) an alpha-particle and (ii) a beta-particle? (e) State Hubble's law and write the significance of Hubble's constant. (f) What is energy crisis? Explain.
(a) A neutron is electrically neutral, so it is not repelled by the positive nuclear charge (there is no Coulomb barrier) and can penetrate and be captured by a nucleus even at low speed. That is why it is the most effective bombarding p...
Answer in brief, any one question. (a) Longitudinal waves are called pressure waves. Why? (b) What is the threshold of hearing? Define one bel.
(a) In a longitudinal wave the medium is alternately compressed and rarefied along the direction of travel. At a compression the local pressure and density rise above normal, and at a rarefaction they fall below normal, so the wave is es...
Answer in brief, any one question. (a) Explain, with a proper sketch, the differences between wavefronts and wavelets. (b) What is polarizing angle? Does it depend on the wavelength of light used?
(a) A wavefront is the continuous locus of all points of a medium that are vibrating in the same phase, for example the spherical or plane surface spreading out from a source. A wavelet, on the other hand, is one of the many small secondary spherical disturbances that, according to Huygens's principle, every point on a wavefront sends out; the forward envelope, or common tangent, of all these wavelets forms the next wavefront. In a sketch one draws a plane (or spherical) wavefront with small semicircular wavelets on it, their common tangent giving the new wavefront.
(b) The polarizing angle, or Brewster angle $\theta_p$, is the angle of incidence at which light reflected from a transparent surface is completely plane-polarised. At this angle the reflected and refracted rays are perpendicular to each other, and the refractive index is $\mu = \tan\theta_p$. Because the refractive index $\mu$ of a medium varies with wavelength (dispersion), the polarizing angle does depend on the wavelength of the light used.
Answer any three questions. (a) Describe the mechanism of current flow in a conductor and derive a relation between current density and drift velocity of electrons. (b) What is Seebeck effect? Explain the variation of thermo-emf with gradual increase in the temperature of the hot junction, keeping the cold junction at 0 degrees C. (c) State the Biot-Savart law. Use this law to find the magnetic field due to a current-carrying circular coil at any point on the axis of the coil. (d) State and explain Faraday's law of electromagnetic induction. Obtain an expression for the emf induced in a rectangular coil rotating in a uniform magnetic field.
(a) In a metal the free electrons move about randomly with high thermal speeds, but their average velocity is zero, so there is no net current. When a field $E$ is applied, each electron acquires a small drift velocity $v_d$ directed opposite to $E$ in the intervals between collisions. In a time $dt$ the charge crossing an area $A$ is $dq = neAv_d,dt$, so the current is $I = neAv_d$, and dividing by the area gives the current density,
$$ \begin{aligned} J &= \frac{I}{A} \ &= nev_d, \end{aligned} $$
where $n$ is the number density of free electrons and $e$ is the electronic charge.
(b) The Seebeck effect is the setting up of an emf, and hence a current, in a closed circuit of two dissimilar metals when its two junctions are kept at different temperatures. Keeping the cold junction at $0^\circ$C and gradually raising the hot-junction temperature $\theta$, the thermo-emf first increases, reaches a maximum at the neutral temperature $\theta_n$, then decreases and becomes zero at the temperature of inversion $\theta_i$, which lies symmetrically about $\theta_n$, and reverses in sign beyond that. The graph of $E$ against $\theta$ is therefore a parabola, $E = \alpha\theta + \tfrac{1}{2}\beta\theta^2$.
(c) The Biot-Savart law states that the magnetic field due to a current element $I,d\vec l$ at a point a distance $r$ away is $dB = \dfrac{\mu_0}{4\pi}\dfrac{I,dl\sin\theta}{r^2}$. For a circular coil of radius $a$ and $N$ turns, at a point on the axis a distance $x$ from the centre, the components of $dB$ perpendicular to the axis cancel while the axial components of all the elements add up, giving
$$B = \frac{\mu_0 N I a^2}{2,(a^2 + x^2)^{3/2}}.$$
At the centre of the coil, where $x = 0$, this reduces to $B = \dfrac{\mu_0 N I}{2a}$.
(d) Faraday's law states that the induced emf equals the negative rate of change of flux linkage, $\varepsilon = -N\dfrac{d\Phi}{dt}$. For a coil of $N$ turns and area $A$ rotating with angular velocity $\omega$ in a uniform field $B$, the flux through it is $\Phi = BA\cos\omega t$, so differentiating gives
$$ \begin{aligned} \varepsilon &= -N\frac{d\Phi}{dt} \ &= NBA,\omega\sin\omega t \ &= \varepsilon_0\sin\omega t, \ \qquad \varepsilon_0 &= NBA\omega. \end{aligned} $$
This is the sinusoidal emf of an a.c. generator, with peak value $\varepsilon_0 = NBA\omega$.
Answer any three questions. (a) What is a Zener diode? Explain its use as a voltage regulator. (b) Discuss the photoelectric effect and derive Einstein's photoelectric equation. What is stopping potential? (c) Define mass defect and binding energy of a nucleus. Draw a graph showing the variation of binding energy per nucleon with atomic (mass) number and interpret the graph. (d) Explain renewable and non-renewable sources of energy with examples, and give an account of the energy consumption scenario in Nepal.
(a) A Zener diode is a heavily doped p-n junction designed to work in reverse breakdown, where it holds a nearly constant voltage $V_Z$. To use it as a voltage regulator it is connected in reverse across the load together with a series resistor $R_s$: any excess input voltage is dropped across $R_s$ while the diode holds $V_Z$, and the Zener current adjusts itself so that the load voltage stays constant despite changes in the input voltage or the load.
(b) The photoelectric effect is the emission of electrons from a metal surface when light of frequency above a threshold value falls on it. Einstein explained it by treating light as photons, each of energy $h\nu$: one photon gives all its energy to one electron, part of it ($W_0 = h\nu_0$, the work function) freeing the electron and the rest appearing as its kinetic energy. This gives Einstein's photoelectric equation,
$$ \begin{aligned} & h\nu = W_0 + \tfrac{1}{2}mv_{max}^2 \ \ & \Rightarrow\ \ & \tfrac{1}{2}mv_{max}^2 = h\nu - h\nu_0 \end{aligned} $$
The stopping potential $V_s$ is the reverse voltage that just stops the fastest photoelectrons, defined by $eV_s = \tfrac{1}{2}mv_{max}^2$.
(c) The mass defect $\Delta m$ is the difference between the sum of the masses of the free constituent nucleons and the actual mass of the nucleus. The binding energy, equal to $\Delta m,c^2$, is the energy needed to split the nucleus into its separate nucleons. The graph of binding energy per nucleon against mass number rises steeply for light nuclei, peaks near iron ($A\approx56$, at about $8.8\ \text{MeV}$), and then falls gently for heavy nuclei. The peak shows that nuclei in the iron region are the most stable; light nuclei release energy by fusion and heavy nuclei by fission as they move towards this peak.
(d) Renewable sources are those replenished naturally and effectively inexhaustible, such as solar, hydro, wind, biomass, and geothermal energy. Non-renewable sources exist in finite amounts and are depleted by use, such as coal, petroleum, natural gas, and nuclear fuel. In Nepal, most of the total energy still comes from traditional biomass (firewood) used for cooking, petroleum products are entirely imported and form the largest commercial share, and hydroelectricity supplies a growing but still limited part of the electricity; the country's huge hydropower potential remains largely undeveloped.
Answer any one question. (a) Describe Newton's formula for the velocity of sound in air. Explain why and how this formula is modified by Laplace. (b) Describe an experiment, with the necessary theory, by which the speed of sound in air is determined using the resonance-tube method.
(a) Newton assumed that sound travels through air isothermally, so the relevant elasticity is the isothermal bulk modulus, equal to the pressure $P$, which gives $$v = \sqrt{\frac{P}{\rho}}$$ This yields about $280\ \text{m s}^{-1}$, rou...
Answer any one question. (a) Define coherent sources of light. Prove that the dark and bright fringes are equally spaced in Young's double-slit experiment. (b) What is a diffraction grating? Discuss the formation of the diffraction pattern due to a diffraction grating.
(a) Coherent sources emit light waves of the same frequency with a constant phase difference. In Young's experiment, with slit separation $d$ and screen distance $D$, the path difference at a point $y$ on the screen is $\dfrac{yd}{D}$. Bright fringes occur where this equals $n\lambda$, at $y_n = \dfrac{n\lambda D}{d}$, and dark fringes at $y_n' = \dfrac{(2n-1)\lambda D}{2d}$. The spacing between consecutive bright (or consecutive dark) fringes is therefore
$$ \begin{aligned} \beta &= y_{n+1} - y_n \ &= \frac{\lambda D}{d}, \end{aligned} $$
which is independent of $n$. Hence all the bright fringes are equally spaced, all the dark fringes are equally spaced, and each dark fringe lies midway between two bright ones, so the fringes are equally spaced.
(b) A diffraction grating is a plate ruled with a very large number of equal, equally spaced parallel slits, with grating element $d = a + b$. When light of wavelength $\lambda$ falls normally on it, each slit diffracts and the beams interfere, and principal maxima occur where
$$d\sin\theta = n\lambda \quad (n = 0, 1, 2,\dots).$$
Because of the large number of slits these maxima are very sharp and bright, separated by broad dark regions, and different wavelengths are sent to different angles, so the grating spreads white light into sharp spectra.
phy-wave-interference
Answer any two questions. (a) In the given circuit, three branches are connected in parallel between two nodes: a 24 V cell in series with 3 ohm, a cell of emf E in series with 2 ohm, and a 7 ohm resistor. What must be the emf E so that the current flowing through the 7 ohm resistor is 1.80 A? Each emf source has negligible internal resistance. (b) A straight horizontal rod of length 20 cm and mass 30 g is placed in a uniform horizontal magnetic field perpendicular to the rod. If a current of 2 A through the rod makes it self-supporting in the magnetic field, calculate the magnetic field. (c) A coil of inductance 0.1 H and negligible resistance is in series with a resistance of 40 ohm. A supply voltage of 50 V (rms) is connected to them. If the voltage across L equals that across R, calculate the voltage across the inductor and the frequency of the supply.
(a) The three branches all share the same node voltage $V$, which appears across the $7\ \Omega$ resistor. Since the current through it is $1.80\ \text{A}$,
$$ \begin{aligned} V &= 1.80\times7 \ &= 12.6\ \text{V} \end{aligned} $$
The current fed into the top node by the $24\ \text{V}$ branch is
$$ \begin{aligned} I_1 &= \frac{24 - V}{3} \ &= \frac{24 - 12.6}{3} \ &= 3.8\ \text{A} \end{aligned} $$
Applying Kirchhoff's current law at the node, $I_1 + I_2 = I_{7\Omega}$, the current in the $E$ branch is
$$ \begin{aligned} I_2 &= 1.80 - 3.8 \ &= -2.0\ \text{A} \end{aligned} $$
the negative sign meaning it actually flows into the $E$ branch. For that branch $V = E - I_2(2)$, so
$$ \begin{aligned} E &= V + 2I_2 \ &= 12.6 + 2(-2.0) \ &= 8.6\ \text{V} \end{aligned} $$
Therefore the required emf is $E = 8.6\ \text{V}$.
(b) For the rod to be self-supporting, the upward magnetic force must balance its weight, $BIL = mg$. With $L = 0.20\ \text{m}$, $m = 0.030\ \text{kg}$, $I = 2\ \text{A}$ and $g = 9.8\ \text{m s}^{-2}$,
$$ \begin{aligned} B &= \frac{mg}{IL} \ &= \frac{(0.030)(9.8)}{(2)(0.20)} \ &= \frac{0.294}{0.40} \ &= 0.735\ \text{T} \end{aligned} $$
(c) Since the voltage across the inductor equals that across the resistor, $V_L = V_R$, which means $X_L = R = 40\ \Omega$. The supply voltage is $V = \sqrt{V_R^2 + V_L^2} = V_R\sqrt{2}$, so
$$ \begin{aligned} V_L &= V_R \ &= \frac{V}{\sqrt{2}} \ &= \frac{50}{\sqrt{2}} \ &= 35.4\ \text{V} \end{aligned} $$
Using $X_L = 2\pi f L$, the supply frequency is
$$ \begin{aligned} f &= \frac{X_L}{2\pi L} \ &= \frac{40}{2\pi(0.1)} \ &= 63.7\ \text{Hz} \end{aligned} $$
Therefore the voltage across the inductor is $35.4\ \text{V}$ and the frequency is $63.7\ \text{Hz}$.
Answer any two questions. (a) An electron moves in a circular path of radius 20 cm in a uniform magnetic field of 2x10^-3 T. Find the speed of the electron and the period of revolution. (Mass of electron = 9.1x10^-31 kg) (b) Calculate the de Broglie wavelength of an electron which has been accelerated through a potential difference of 200 V. (Mass of electron = 9.1x10^-31 kg, Planck's constant h = 6.6x10^-34 Js) (c) The isotope Ra-226 undergoes alpha decay with a half life of 1620 years. What is the activity of 1 g of Ra-226? (Avogadro number = 6.023x10^23 /mol)
(a) For the electron moving in a circle, the magnetic force provides the centripetal force, so the radius is $r = \dfrac{mv}{eB}$. With $e = 1.6\times10^{-19}\ \text{C}$, $B = 2\times10^{-3}\ \text{T}$ and $r = 0.20\ \text{m}$, the speed...
A car is approaching a cliff at a speed of 20 m/s. The driver sounds a whistle of frequency 800 Hz. What will be the frequency of the echo as heard by the car driver? (Velocity of sound in air = 350 m/s)
The car acts as both source and observer, moving toward the cliff at $vs = 20\ \text{m s}^{-1}$, the whistle frequency is $f = 800\ \text{Hz}$, and the speed of sound is $v = 350\ \text{m s}^{-1}$. First the cliff receives the sound; sin...
A plane mirror is placed at the centre of a concave mirror having a radius of curvature 40 m. The plane mirror rotates at 2600 revolutions per second. Calculate the angle between a ray incident on the plane mirror and the ray reflected from it after the light has travelled to the concave mirror and back to the plane mirror. (Speed of light = 3x10^8 m/s)
We are given that the plane mirror sits at the centre of curvature of the concave mirror, so the plane-to-concave distance equals the radius of curvature, $d = 40\ \text{m}$; the plane mirror rotates at $n = 2600\ \text{rev s}^{-1}$, and the speed of light is $c = 3\times10^{8}\ \text{m s}^{-1}$.
The time taken for light to travel to the concave mirror and back to the plane mirror is
$$ \begin{aligned} t &= \frac{2d}{c} \ &= \frac{2(40)}{3\times10^{8}} \ &= 2.67\times10^{-7}\ \text{s} \end{aligned} $$
During this time the plane mirror, rotating with angular speed $\omega = 2\pi n$, turns through an angle
$$ \begin{aligned} \phi &= \omega t \ &= 2\pi(2600)(2.67\times10^{-7}) \ &= 4.36\times10^{-3}\ \text{rad} \end{aligned} $$
A rotation $\phi$ of the mirror turns the reflected ray through $2\phi$, so the angle between the original incident ray and the finally reflected ray is
$$ \begin{aligned} \theta &= 2\phi \ &= 8.71\times10^{-3}\ \text{rad} \ &= 0.50^\circ \end{aligned} $$
(a) The maximum resistance comes from connecting all wires in series, giving , while the minimum comes from connecting them all in parallel, giving . The ratio is therefore $$ \begin{aligned} \frac{R{max}}{...
(a) A wavefront is the continuous locus of all points of a medium that are vibrating in the same phase, for example the spherical or plane surface spreading out from a source. A wavelet, on the other hand, is one of the many small secondary spherical disturbances that, according to Huygens's principle, every point on a wavefront sends out; the forward envelope, or common tangent, of all these wavelets forms the next wavefront. In a sketch one draws a plane (or spherical) wavefront with small semicircular wavelets on it, their common tangent giving the new wavefront.
(b) The polarizing angle, or Brewster angle , is the angle of incidence at which light reflected from a transparent surface is completely plane-polarised. At this angle the reflected and refracted rays are perpendicular to each other, and the refractive index is . Because the refractive index of a medium varies with wavelength (dispersion), the polarizing angle does depend on the wavelength of the light used.
(a) In a metal the free electrons move about randomly with high thermal speeds, but their average velocity is zero, so there is no net current. When a field is applied, each electron acquires a small drift velocity directed opposite to in the intervals between collisions. In a time the charge crossing an area is , so the current is , and dividing by the area gives the current density,
where is the number density of free electrons and is the electronic charge.
(b) The Seebeck effect is the setting up of an emf, and hence a current, in a closed circuit of two dissimilar metals when its two junctions are kept at different temperatures. Keeping the cold junction at C and gradually raising the hot-junction temperature , the thermo-emf first increases, reaches a maximum at the neutral temperature , then decreases and becomes zero at the temperature of inversion , which lies symmetrically about , and reverses in sign beyond that. The graph of against is therefore a parabola, .
(c) The Biot-Savart law states that the magnetic field due to a current element at a point a distance away is . For a circular coil of radius and turns, at a point on the axis a distance from the centre, the components of perpendicular to the axis cancel while the axial components of all the elements add up, giving
At the centre of the coil, where , this reduces to .
(d) Faraday's law states that the induced emf equals the negative rate of change of flux linkage, . For a coil of turns and area rotating with angular velocity in a uniform field , the flux through it is , so differentiating gives
This is the sinusoidal emf of an a.c. generator, with peak value .
(a) A Zener diode is a heavily doped p-n junction designed to work in reverse breakdown, where it holds a nearly constant voltage . To use it as a voltage regulator it is connected in reverse across the load together with a series resistor : any excess input voltage is dropped across while the diode holds , and the Zener current adjusts itself so that the load voltage stays constant despite changes in the input voltage or the load.
(b) The photoelectric effect is the emission of electrons from a metal surface when light of frequency above a threshold value falls on it. Einstein explained it by treating light as photons, each of energy : one photon gives all its energy to one electron, part of it (, the work function) freeing the electron and the rest appearing as its kinetic energy. This gives Einstein's photoelectric equation,
The stopping potential is the reverse voltage that just stops the fastest photoelectrons, defined by .
(c) The mass defect is the difference between the sum of the masses of the free constituent nucleons and the actual mass of the nucleus. The binding energy, equal to , is the energy needed to split the nucleus into its separate nucleons. The graph of binding energy per nucleon against mass number rises steeply for light nuclei, peaks near iron (, at about ), and then falls gently for heavy nuclei. The peak shows that nuclei in the iron region are the most stable; light nuclei release energy by fusion and heavy nuclei by fission as they move towards this peak.
(d) Renewable sources are those replenished naturally and effectively inexhaustible, such as solar, hydro, wind, biomass, and geothermal energy. Non-renewable sources exist in finite amounts and are depleted by use, such as coal, petroleum, natural gas, and nuclear fuel. In Nepal, most of the total energy still comes from traditional biomass (firewood) used for cooking, petroleum products are entirely imported and form the largest commercial share, and hydroelectricity supplies a growing but still limited part of the electricity; the country's huge hydropower potential remains largely undeveloped.
(a) Newton assumed that sound travels through air isothermally, so the relevant elasticity is the isothermal bulk modulus, equal to the pressure , which gives This yields about , rou...
(a) Coherent sources emit light waves of the same frequency with a constant phase difference. In Young's experiment, with slit separation and screen distance , the path difference at a point on the screen is . Bright fringes occur where this equals , at , and dark fringes at . The spacing between consecutive bright (or consecutive dark) fringes is therefore
which is independent of . Hence all the bright fringes are equally spaced, all the dark fringes are equally spaced, and each dark fringe lies midway between two bright ones, so the fringes are equally spaced.
(b) A diffraction grating is a plate ruled with a very large number of equal, equally spaced parallel slits, with grating element . When light of wavelength falls normally on it, each slit diffracts and the beams interfere, and principal maxima occur where
Because of the large number of slits these maxima are very sharp and bright, separated by broad dark regions, and different wavelengths are sent to different angles, so the grating spreads white light into sharp spectra.
(a) The three branches all share the same node voltage , which appears across the resistor. Since the current through it is ,
The current fed into the top node by the branch is
Applying Kirchhoff's current law at the node, , the current in the branch is
the negative sign meaning it actually flows into the branch. For that branch , so
Therefore the required emf is .
(b) For the rod to be self-supporting, the upward magnetic force must balance its weight, . With , , and ,
(c) Since the voltage across the inductor equals that across the resistor, , which means . The supply voltage is , so
Using , the supply frequency is
Therefore the voltage across the inductor is and the frequency is .
(a) For the electron moving in a circle, the magnetic force provides the centripetal force, so the radius is . With , and , the speed...
The car acts as both source and observer, moving toward the cliff at , the whistle frequency is , and the speed of sound is . First the cliff receives the sound; sin...
We are given that the plane mirror sits at the centre of curvature of the concave mirror, so the plane-to-concave distance equals the radius of curvature, ; the plane mirror rotates at , and the speed of light is .
The time taken for light to travel to the concave mirror and back to the plane mirror is
During this time the plane mirror, rotating with angular speed , turns through an angle
A rotation of the mirror turns the reflected ray through , so the angle between the original incident ray and the finally reflected ray is