Physics
भौतिक विज्ञान · Class 12 · Code 1021 (CDC Phy.102)
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chapters done
- Mechanics
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The syllabus asks for
- Equation of angular motion; Relation between linear and angular kinematics
- Kinetic energy of rotation of rigid body
- Moment of inertia; Radius of gyration
- Moment of inertia of a uniform rod
- Torque and angular acceleration for a rigid body
- Work and power in rotational motion
- Angular momentum; conservation of angular momentum
Key points
- For constant α: ω = ω0 + α t, θ = ω0 t + (1)/(2)α t^2, ω^2 = ω0^2 + 2αθ; and s = rθ, v = rω, at = rα, ac = rω^2.
- Rotational kinetic energy Ek = (1)/(2)Iω^2, where I = Σ mi ri^2 = ∫ r^2dm is the moment of inertia.
- Radius of gyration: I = Mk^2, so k = √I/M. Parallel axis: I = Icm + Md^2; perpendicular axis (laminae): Iz = Ix + Iy.
- Uniform rod of mass M, length L: I = ML^2/12 about the centre and ML^2/3 about one end.
- Torque τ = rFsinφ and τ = Iα, the rotational form of F = ma.
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The syllabus asks for
- Equation of simple harmonic motion (SHM)
- Energy in SHM
- Application of SHM: vertical oscillation of mass suspended from coiled spring
- Angular SHM; simple pendulum
- Oscillatory motion: Damped oscillation, Forced oscillation and resonance
Key points
- SHM: a = -ω^2x, with x = Asin(ω t + φ), v = Aωcos(ω t+φ) = ω√A^2-x^2 and T = 2π/ω = 2π√m/k.
- Speed is maximum (Aω) at the mean position; acceleration is maximum (ω^2A) at the extremes. SHM is the projection of uniform circular motion on a diameter.
- U = (1)/(2)mω^2x^2, K = (1)/(2)mω^2(A^2-x^2), and the total E = (1)/(2)mω^2A^2 = (1)/(2)kA^2 is constant.
- Mass on a vertical spring: mg = ke and T = 2π√m/k = 2π√e/g; the weight only shifts the mean position.
- Angular SHM: τ = -cθ gives T = 2π√I/c. Simple pendulum: T = 2π√L/g for small amplitude, independent of the mass of the bob.
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The syllabus asks for
- Fluid statics: Pressure in a fluid; Buoyancy
- Surface tension: Theory of surface tension; Surface energy
- Angle of contact, capillarity and its applications
- Fluid Dynamics: Newton's formula for viscosity in a liquid; Coefficient of viscosity
- Poiseuille's formula and its application
- Stokes law and its applications
- Equation of continuity and its applications
- Bernoulli's equation and its applications
Key points
- P = hρ g (gauge), P = P0 + hρ g (absolute); pressure depends on depth only, and Pascal's law transmits it undiminished.
- Upthrust U = Vρ g = weight of fluid displaced; a floating body has Vs/V = ρb/ρl.
- T = F/L (N m⁻¹) equals the surface energy W/Δ A (J m⁻²). Excess pressure: 2T/r in a drop, 4T/r in a soap bubble.
- Capillary rise h = 2Tcosθ/rρ g, so h ∝ 1/r.
- Viscosity F = η A dv/dx, η in Pa s, [ML^-1T^-1].
- Heat and Thermodynamics
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The syllabus asks for
- Thermodynamic systems
- Work done during volume change
- Heat and work; Internal energy and First law of thermodynamics
- Thermodynamic processes: Adiabatic, isochoric, isothermal and isobaric
- Heat capacities of an ideal gas at constant pressure and volume and relation between them
- Isothermal and Adiabatic processes for an ideal gas
Key points
- A system exchanges matter and energy with its surroundings across a boundary; open, closed and isolated systems differ in what may cross it. P, V, T and U are state functions; Q and W are path functions.
- Work done by a gas is W = ∫ P dV, the area under the P–V curve; positive for expansion, negative for compression.
- First law: Q = Δ U + W, with Q positive for heat absorbed and W positive for expansion. For an ideal gas U depends only on T.
- Isochoric: W=0, Q=Δ U. Isobaric: W = PΔ V. Isothermal: Δ U = 0, Q = W. Adiabatic: Q = 0, Δ U = -W. Cyclic: Δ U = 0, Q = W = area of loop.
- Mayer's relation: Cp - Cv = R, so Cv = R/(γ-1) and Cp = γ R/(γ-1). Here γ = 1.67, 1.40 and 1.33 for mono-, di- and polyatomic gases.
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The syllabus asks for
- Thermodynamic systems and direction of thermodynamic processes
- Second law of thermodynamics
- Heat engines
- Internal combustion engines: Otto cycle, Diesel cycle, Carnot cycle
- Refrigerator
- Entropy and disorder (introduction only)
Key points
- Real processes run one way only. A reversible process is quasi-static and free of all dissipative effects; no real process is reversible.
- Kelvin–Planck: no cyclic device can convert heat from a single reservoir entirely into work. Clausius: no self-acting cyclic device can move heat from a colder to a hotter body. The two statements are equivalent.
- Heat engine: W = Q1 - Q2 and η = W/Q1 = 1 - Q2/Q1. A sink is compulsory, so η < 1 always.
- Otto cycle (petrol): two adiabatics and two isochorics, η = 1 - r^-(γ-1). Diesel cycle: heat added isobarically, allowing a much larger r.
- Carnot cycle: two isothermals and two adiabatics, all reversible, with η = 1 - T2/T1 — the maximum possible for the given temperatures, and independent of the working substance (Carnot's theorem).
- Waves and Optics
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The syllabus asks for
- Progressive waves
- Mathematical description of a wave
- Stationary waves
Key points
- A progressive wave carries energy and momentum through a medium without carrying the medium. Transverse waves vibrate perpendicular to the direction of travel, longitudinal waves parallel to it.
- v = fλ = λ/T for every wave; in a given medium v is fixed, so raising f shortens λ.
- Wave equation: y = asin(ω t - kx) = asin 2π(t/T - x/λ), with ω = 2π/T, k = 2π/λ and v = ω/k. Use +kx for a wave travelling in the -x direction.
- Phase difference and path difference are linked by Δφ = (2π/λ)Δ x.
- Particle velocity vp = aωcos(ω t - kx), maximum aω; it is not the wave velocity.
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The syllabus asks for
- Speed of wave motion; Velocity of sound in solid and liquid
- Velocity of sound in gas
- Laplace's correction
- Effect of temperature, pressure, humidity on velocity of sound
Key points
- Every wave obeys v=fλ, but the speed itself is set by the medium: v=√E/ρ, elasticity over inertia.
- Solid rod: v=√Y/ρ (≈ 5060 m s^-1 in steel). Liquid: v=√B/ρ (≈ 1480 m s^-1 in water). Fluids carry only longitudinal sound; solids carry longitudinal and transverse waves.
- Newton's formula: assuming isothermal compressions, Biso=P and v=√P/ρ, giving 280 m s⁻¹ for air — 16 % too low.
- Laplace's correction: the compressions are adiabatic, so Badi=γ P and v=√γ P/ρ = 331 m s^-1, which matches experiment.
- Eliminating density gives v=√γ RT/M: the speed depends on temperature and on the gas, never on the pressure.
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The syllabus asks for
- Stationary waves in closed and open pipes
- Harmonics and overtones in closed and open organ pipes
- End correction in pipes
- Velocity of transverse waves along a stretched string
- Vibration of string and overtones
- Laws of vibration of fixed string
Key points
- A stationary wave forms when incident and reflected waves superpose. Closed end → displacement node; open end → displacement antinode. Adjacent nodes are λ/2 apart.
- Closed pipe: L=(2n-1)λ/4, so fn = (2n-1)v/4L — odd harmonics only. The 1st overtone is the 3rd harmonic.
- Open pipe: L=nλ/2, so fn = nv/2L — all harmonics. An open pipe sounds one octave above a closed pipe of the same length and gives a richer note.
- End correction e = 0.6r: closed pipe f1 = v/4(L+e), open pipe f1 = v/2(L+2e).
- Resonance tube: v = 2f(l2-l1) and e = (l2-3l1)/2.
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The syllabus asks for
- Sound waves: Pressure amplitude
- Characteristics of sound: Intensity, loudness, quality and pitch
- Doppler's effect
Key points
- Excess pressure Δ P = -B partial y/partial x; the pressure amplitude is P0 = Bak = ρ vω a = 2πρ v f a.
- The pressure wave is λ/4 out of phase with the displacement wave: a displacement node is a pressure antinode.
- Intensity I = (1)/(2)ρ vω^2a^2 = P0^2/2ρ v, in W m⁻²; for a point source I = P/4π r^2, so I∝ 1/r^2.
- Intensity level β = 10log10(I/I0) dB with I0 = 10^-12 W m^-2. Doubling I adds 3 dB; doubling the distance subtracts 6 dB.
- Loudness (Weber–Fechner, L = klog I) is the sensation; pitch is set by frequency; quality is set by the overtones present, i.e. by the waveform.
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The syllabus asks for
- Huygen's principle
- Reflection and Refraction according to wave theory
Key points
- A wavefront is the locus of points vibrating in the same phase; a ray is the normal to the wavefront. Wavefronts may be spherical, cylindrical or plane.
- Huygens' principle: every point of a wavefront is a source of secondary wavelets of radius vt; the new wavefront is their forward envelope. Backward wavelets are suppressed by the obliquity factor K = (1)/(2)(1+cosθ).
- Reflection: BC = AD = ct gives sin i/sin r = 1, so i = r, and the incident ray, reflected ray and normal are coplanar.
- Refraction: BC = v1t, AD = v2t give dfracsin isin r = dfracv1v2 = dfracn2n1, i.e. n1sin i = n2sin r.
- On refraction the frequency is unchanged; the speed and wavelength both fall by the factor n: v = c/n and λm = λ0/n.
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The syllabus asks for
- Phenomenon of Interference: Coherent sources
- Young's double slit experiment
Key points
- Superposition gives I = I1 + I2 + 2√I1I2cosφ, with φ = 2πΔ/λ.
- Bright when Δ = nλ; dark when Δ = (2n-1)λ/2. For equal sources I = 4I0cos^2(φ/2), with Imax = 4I0, Imin = 0.
- Imax:Imin = (√I1+√I2)^2 : (√I1-√I2)^2.
- Coherent sources have the same frequency and a constant phase difference; they must be obtained from one source, by division of wavefront or of amplitude.
- In Young's experiment Δ = yd/D, bright fringes at yn = nλ D/d, dark at yn = (2n-1)λ D/2d.
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The syllabus asks for
- Diffraction from a single slit
- Diffraction pattern of image; Diffraction grating
- Resolving power of optical instruments
Key points
- Diffraction is the bending of light round edges, noticeable only when the aperture is comparable with λ. Fraunhofer diffraction uses plane waves.
- Single slit minima: asinθ = nλ for n = ±1, ±2, dots; secondary maxima near asinθ = (n+(1)/(2))λ, of relative intensity 4.7%, 1.7%, …
- Intensity: I = I0(sinβ/β)^2 with β = π asinθ/λ.
- Central maximum: angular width 2λ/a, linear width 2λ D/a — it gets wider as the slit gets narrower.
- Grating element d = 1/N; grating equation dsinθ = nλ; highest order nmax = d/λ; in each order violet is deviated least.
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The syllabus asks for
- Phenomenon of polarization
- Brewster's law; transverse nature of light
- Polaroid
Key points
- Unpolarized light vibrates in all directions perpendicular to the ray; plane polarized light vibrates in one plane only. The plane of polarization is perpendicular to the plane of vibration.
- Polarized light is produced by reflection, refraction through a pile of plates, selective absorption (Polaroid), double refraction (Nicol prism) and scattering.
- Degree of polarization P = (Imax-Imin)/(Imax+Imin).
- Brewster's law: n = tanθp, with θp + r = 90^°; the reflected and refracted rays are then perpendicular and the reflected beam is fully plane polarized.
- Brewster's angle (tan^-1n, rarer to denser) is not the critical angle (sin^-1(1/n), denser to rarer).
- Electricity and Magnetism
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The syllabus asks for
- Kirchhoff's law
- Wheatstone bridge circuit; Meter bridge
- Potentiometer: Comparison of e.m.f.; measurement of internal resistance of a cell
- Super conductors; Perfect conductors
- Conversion of galvanometer into voltmeter and ammeter; Ohmmeter
- Joule's law
Key points
- Kirchhoff's junction law Σ I = 0 expresses conservation of charge; the loop law Σ E = Σ IR expresses conservation of energy.
- A Wheatstone bridge is balanced when Ig = 0, and then P/Q = R/S. The condition is independent of the cell and of the galvanometer.
- Metre bridge: X = R l/(100-l), with l measured from the end next to X. Keep l near 50 cm and interchange X and R to cancel end errors.
- Potentiometer: V = kl with k = VAB/L. Comparison of e.m.f. E1/E2 = l1/l2; internal resistance r = R(l1-l2)/l2. At balance the cell supplies no current, so the true e.m.f. is measured.
- A superconductor has ρ = 0 below Tc and expels magnetic flux (Meissner effect); a merely perfect conductor would trap the flux instead.
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The syllabus asks for
- Seebeck effect; Thermocouples
- Peltier effect: Variation of thermoelectric e.m.f. with temperature; Thermopile
Key points
- Seebeck effect: two dissimilar metals, two junctions at different temperatures, an e.m.f. appears. It depends only on the metals and on the temperature difference.
- Seebeck series Sb, Fe, Cd, Zn, Ag, Au, Cr, Sn, Pb, Hg, Mn, Cu, Pt, Co, Ni, Bi: the current flows from the earlier metal to the later one through the cold junction, and the further apart the metals, the greater the e.m.f.
- Peltier effect: a current through a junction evolves heat at one junction and absorbs it at the other; H = π It, proportional to I and reversible, unlike Joule heat I^2Rt.
- E = αθ + (1)/(2)βθ^2 with the cold junction at 0 ^°C; thermoelectric power S = dE/dθ = α + βθ.
- Neutral temperature θn = -α/β (where E is maximum, fixed by the metals alone); temperature of inversion θi = 2θn - θc (where E returns to zero and reverses).
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The syllabus asks for
- Magnetic field lines and magnetic flux; Oersted's experiment
- Force on moving charge; Force on a conductor
- Force and Torque on rectangular coil; Moving coil galvanometer
- Hall effect
- Magnetic field of a moving charge
- Biot and Savart law and application to circular coil, long straight conductor, long solenoid
- Ampere's law and applications to long straight conductor, straight solenoid, toroidal solenoid
- Force between two parallel conductors carrying current; definition of ampere
Key points
- Magnetic flux Phi = BAcosθ (weber); field lines are closed loops, so ointB· dA = 0 — there are no magnetic monopoles.
- Oersted: a current produces a magnetic field. Direction by the right-hand grip rule (or SNOW).
- Force on a moving charge F = qvtimesB, F = qvBsinθ; it does no work. Perpendicular entry gives a circle with r = mv/qB, T = 2π m/qB, independent of speed.
- Force on a conductor F = BILsinθ; direction by Fleming's left-hand rule.
- Torque on a coil τ = NBIAsinθ = NBIAcosα, with dipole moment m = NIA. A radial field makes sinθ = 1, so a moving-coil galvanometer has varphi = (NBA/c)I and a uniform scale.
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The syllabus asks for
- Magnetic field lines and magnetic flux
- Flux density in magnetic material; Relative permeability; Susceptibility
- Hysteresis
- Dia-, para- and ferro-magnetic materials
Key points
- Magnetic flux Phi = BAcosθ (weber); B = Phi/A is the flux density (tesla); ointB· dA = 0 since field lines are closed loops.
- The magnetising field is H = NI/l (A m⁻¹); magnetisation is M = m/V (A m⁻¹); inside matter B = μ0(H+M).
- chim = M/H, μ = B/H, μr = μ/μ0 and μr = 1 + chim. Both chim and μr are dimensionless.
- Hysteresis is the lag of B behind H. Retentivity Br is the flux density left when H = 0; coercivity Hc is the reverse field that makes B = 0.
- Energy dissipated per unit volume per cycle equals the loop area, oint H dB (J m⁻³); the hysteresis power loss is (area) × V × f.
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The syllabus asks for
- Faraday's laws; Induced electric fields
- Lenz's law; Motional electromotive force
- A.C. generators; Eddy currents
- Self-inductance and mutual inductance
- Energy stored in an inductor
- Transformer
Key points
- Faraday: an e.m.f. appears whenever flux linkage changes, e = -N dPhi/dt; the charge circulated is q = NΔPhi/R, independent of the time taken.
- A changing B produces a non-conservative induced electric field, ointE· dl = -dPhi/dt.
- Lenz: the induced current opposes the change producing it — a statement of energy conservation, carried by the minus sign.
- Motional e.m.f. e = Blv (or Blvsinθ); the retarding force is B^2l^2v/R and Fv = I^2R.
- A.C. generator: Phi = BAcosω t gives e = NBAωsinω t with peak value e0 = NBAω.
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The syllabus asks for
- Peak and rms value of AC current and voltage
- AC through a resistor, a capacitor and an inductor
- Phasor diagram
- Series circuits containing combination of resistance, capacitance and inductance
- Series resonance; quality factor
- Power in AC circuits: power factor
Key points
- For i = I0sinω t: Irms = I0/√2 = 0.707I0, Iav (half cycle) = 2I0/π = 0.637I0, and the full-cycle mean is zero. Meters read r.m.s.
- Resistor: i in phase with v. Inductor: i lags by 90^°, XL = 2π fL. Capacitor: i leads by 90^°, XC = 1/2π fC.
- A phasor is a vector of length equal to the peak (or r.m.s.) value, rotating at ω; sinusoids of the same frequency add like vectors.
- Series LCR: Z = √R^2+(XL-XC)^2 and tanφ = (XL-XC)/R; V = √VR^2+(VL-VC)^2.
- Resonance: XL = XC, so f0 = 1/2π√LC, Zmin = R, Imax = V/R and φ = 0 (acceptor circuit).
- Modern Physics
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The syllabus asks for
- Millikan's oil drop experiment
- Motion of electron beam in electric and magnetic fields
- Thomson's experiment to determine specific charge of electrons
Key points
- Millikan balanced the apparent weight of a charged oil drop against an electric force: q = mgd/V for a stationary drop, or q = 6πη r v1 d/V with r = √9η v1/2(ρ-σ)g.
- Every measured charge is an integral multiple of e = 1.60×10^-19 C: charge is quantised.
- An electron accelerated through Va has speed v = √2eVa/m.
- In a transverse electric field the path is a parabola with deflection y = eEL^2/2mv^2 = VdL^2/4Vad at the edge of the plates.
- In a transverse magnetic field the path is a circle, r = mv/eB, period T = 2π m/eB; the magnetic force does no work, so the speed is unchanged.
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The syllabus asks for
- Quantum nature of radiation
- Einstein's photoelectric equation; Stopping potential
- Measurement of Planck's constant
Key points
- Radiation is emitted and absorbed in quanta: a photon has E = hf = hc/λ, p = h/λ, zero rest mass, and travels at c.
- Intensity fixes the number of photons per second; frequency fixes the energy of each one.
- Photoelectric emission occurs only above a threshold frequency f0, is instantaneous, gives a current proportional to intensity, and gives a maximum kinetic energy proportional to (f-f0).
- Einstein's equation: hf = φ0 + Kmax, with φ0 = hf0 = hc/λ0.
- Stopping potential: eV0 = Kmax, so V0 = (h/e)f - φ0/e; V0 is independent of intensity.
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The syllabus asks for
- P-N Junction
- Semiconductor diode: Characteristics in forward and reverse bias
- Full wave rectification
- Logic gates: NOT, OR, AND, NAND and NOR
Key points
- Diffusion across a p-n junction leaves a depletion region of immobile ions and a barrier potential VB (0.3 V Ge, 0.7 V Si) that stops further diffusion.
- Forward bias lowers the barrier, narrows the depletion layer and gives a large majority-carrier current; reverse bias does the opposite and leaves only a microamp reverse saturation current until breakdown.
- The diode characteristic is non-linear: no current below the knee voltage, then a steep rise. Dynamic resistance rd = Δ V/Δ I.
- Half-wave: Idc=Im/π, ηmax=40.6%, ripple 1.21, output 50 Hz.
- Full-wave: Idc=2Im/π, Vdc=2Vm/π, Irms=Im/√2, η = (8/π^2)RL/(RL+rf), maximum 81.2%, ripple 0.48, output 100 Hz.
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The syllabus asks for
- Bohr's theory of hydrogen atom
- Spectral series; Excitation and ionization potentials
- Energy level; Emission and absorption spectra
- De Broglie Theory; Duality
- Uncertainty principle
- X-rays: Nature and production; uses
- X-rays diffraction; Bragg's law
Key points
- Bohr: mvr = nh/2π; rn = varepsilon0h^2n^2/π me^2 = 0.529 n^2 Å; vn = c/137n; En = -13.6/n^2 eV (multiply by Z^2, divide rn by Z, for hydrogen-like ions).
- hν = Ei - Ef gives 1/λ = R(1/nf^2 - 1/ni^2), R = 1.097×10^7 m⁻¹. Series: Lyman (UV, nf=1), Balmer (visible), Paschen, Brackett, Pfund (IR).
- Hydrogen: first excitation potential 10.2 V, ionization potential 13.6 V. Emission gives bright lines, absorption dark lines at the same wavelengths.
- De Broglie: λ = h/p = 12.27/√V Å for an accelerated electron; 2π r = nλ reproduces Bohr's quantization.
- Uncertainty: Δ x Δ p ≥ h/4π and Δ E Δ t ≥ h/4π.
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The syllabus asks for
- Alpha-particles, Beta-particles, Gamma rays
- Laws of radioactive disintegration
- Half-life, mean-life and decay constant
- Geiger-Muller Tube
- Carbon dating
- Medical use of nuclear radiation and possible health hazard
Key points
- Binding energy per nucleon peaks near A ≈ 56 at about 8.8 MeV; nuclei move towards the peak by fusing, splitting or emitting α-particles.
- α = ⁴₂He (A-4, Z-2); β^- = electron created when n → p (Z+1); γ = photon (no change). Ionizing power α > β > γ; penetrating power is the reverse.
- Q = Δ m × 931.5 MeV is the energy released in a decay.
- Decay law: dN/dt = -λ N gives N = N0e^-λ t and A = λ N = A0e^-λ t. 1 Ci = 3.7×10^10 Bq.
- T1/2 = 0.693/λ; τ = 1/λ = 1.44 T1/2; after n half-lives N/N0 = (1/2)^n.
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The syllabus asks for
- Seismology: Surface waves (Rayleigh and Love waves); Internal waves (S and P-waves); Wave patterns of Gorkha Earthquake 2015
- Gravitational Wave; Nanotechnology; Higgs Boson
Key points
- Body waves: P (longitudinal, ~6 km s⁻¹, passes through liquids) and S (transverse, ~3.5 km s⁻¹, blocked by liquids). Surface waves: Love (horizontal transverse) and Rayleigh (rolling ellipse, largest amplitude). Arrival order P, S, Love, Rayleigh.
- Epicentral distance from the S–P interval: d = Δ t vPvS/(vP - vS); three stations fix the epicentre.
- Gorkha: 25 April 2015, Mw 7.8, focus ~15 km deep near Barpak, rupture ~140 km eastwards on the Main Himalayan Thrust; PGA in Kathmandu only ~0.16g but strong 4–5 s basin resonance; about 8,970 deaths.
- Gravitational waves are ripples of spacetime travelling at c, of strain h = Δ L/L ≈ 10^-21. LIGO's 4 km interferometers detected GW150914 on 14 September 2015 (36 + 29 → 62 solar masses, 3 radiated).
- Nanotechnology works between 1 and 100 nm, where surface-to-volume ratio (6/L) and quantum confinement change behaviour: fullerenes, nanotubes, graphene, quantum dots.
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The paper
3hr, FM 75 written (+25 internal)
| Section | Questions | Marks each | Total |
|---|---|---|---|
| Group A MCQ | 11 | 1 | 11 |
| Group B short | 8 | 5 | 40 |
| Group C long | 3 | 8 | 24 |
Where the hours go
Teaching hours are the board's guide to how much of the paper each part carries.
- Electricity and Magnetism35 h
- Modern Physics33 h
- Waves and Optics26 h
- Mechanics22 h
- Heat and Thermodynamics12 h