ISC Class 12 Physics Syllabus

State Kirchhoff's two circuit laws.

Junction rule (KCL): the algebraic sum of currents at any junction is zero (conservation of charge). Loop rule (KVL): the algebraic sum of potential differences around any closed loop is zero (conservation of energy).

Write the condition for balance of a Wheatstone bridge.

The bridge is balanced (no galvanometer current) when P/Q = R/S, i.e., the ratio of resistances in the two arms is equal.

Distinguish between EMF and terminal potential difference of a cell.

EMF (ε) is the maximum potential difference between the terminals when no current is drawn (open circuit). Terminal p.d. V = ε − Ir is the voltage across the terminals when current I flows through internal resistance r.

State the Biot–Savart law for the magnetic field due to a current element.

dB = (μ₀/4π)·(I dl sinθ)/r², where the field is perpendicular to both the current element and the position vector; direction given by the right-hand rule. μ₀ = 4π×10⁻⁷ T·m/A.

Give the magnetic field at the centre of a circular current loop of radius r carrying current I.

B = μ₀I/2r, directed along the axis (right-hand rule).

State Ampère's circuital law.

The line integral of the magnetic field around a closed loop equals μ₀ times the net current enclosed: ∮B·dl = μ₀I_enclosed.

Write the force on a charge moving in a magnetic field (Lorentz force).

F = qv × B, magnitude F = qvB sinθ, where θ is the angle between velocity and field. The force is perpendicular to both v and B.

Give the force per unit length between two parallel current-carrying wires.

F/L = μ₀I₁I₂/(2πd). Wires carrying currents in the same direction attract; opposite directions repel.

What is the magnetic field inside a long solenoid with n turns per unit length carrying current I?

B = μ₀nI, uniform and directed along the axis. (Outside an ideal solenoid B ≈ 0.)

Define magnetic dipole moment of a current loop.

m = NIA, where N is number of turns, I the current, and A the loop area. It is a vector directed along the axis given by the right-hand rule. Unit: A·m².

Classify magnetic materials into three types with one key property of each.

Diamagnetic (weakly repelled, relative permeability μ_r < 1, e.g., bismuth); Paramagnetic (weakly attracted, μ_r slightly > 1, e.g., aluminium); Ferromagnetic (strongly attracted, μ_r >> 1, e.g., iron, exhibit hysteresis).

Define magnetic susceptibility and its relation to relative permeability.

Magnetic susceptibility χ = M/H (ratio of magnetisation to magnetising field intensity). It relates to relative permeability by μ_r = 1 + χ.

State Faraday's laws of electromagnetic induction.

First law: an EMF is induced in a circuit whenever the magnetic flux linked with it changes. Second law: the induced EMF equals the negative rate of change of magnetic flux: ε = −dΦ/dt (for N turns, ε = −N dΦ/dt).

State Lenz's law and the conservation principle it expresses.

The direction of induced current is such that it opposes the change in magnetic flux producing it (the minus sign in Faraday's law). It is a consequence of the conservation of energy.

Give the expression for motional EMF for a rod of length l moving with velocity v perpendicular to field B.

ε = Blv. If the rod moves at angle θ to B, ε = Blv sinθ.

Define self-inductance and mutual inductance.

Self-inductance L is the property by which a changing current in a coil induces an EMF in itself: ε = −L dI/dt. Mutual inductance M relates the EMF induced in one coil to the rate of change of current in a neighbouring coil: ε₂ = −M dI₁/dt. Unit: henry (H).

Write the formula for energy stored in an inductor.

U = ½LI².

For an AC source, relate the RMS value to the peak value of current and voltage.

I_rms = I₀/√2 ≈ 0.707 I₀ and V_rms = V₀/√2, where I₀ and V₀ are peak (amplitude) values.

Define inductive reactance and capacitive reactance.

Inductive reactance X_L = ωL = 2πfL (increases with frequency). Capacitive reactance X_C = 1/(ωC) = 1/(2πfC) (decreases with frequency). Both have unit ohm.

Write the impedance of a series LCR circuit and the resonance condition.

Impedance Z = √[R² + (X_L − X_C)²]. Resonance occurs when X_L = X_C, giving Z = R (minimum) and resonant frequency f₀ = 1/(2π√(LC)).

Define power factor in an AC circuit and give average power consumed.

Power factor = cosφ = R/Z, where φ is the phase angle between voltage and current. Average power P = V_rms I_rms cosφ.

What is displacement current and how did Maxwell define it?

Displacement current is a current-like quantity arising from a changing electric field: I_d = ε₀ dΦ_E/dt. Maxwell introduced it to make Ampère's law consistent, explaining the magnetic field between capacitor plates.

State the speed of electromagnetic waves in vacuum and its relation to ε₀ and μ₀.

c = 1/√(μ₀ε₀) ≈ 3×10⁸ m/s. EM waves are transverse, with E and B perpendicular to each other and to the direction of propagation.

List the electromagnetic spectrum in order of increasing frequency.

Radio waves → Microwaves → Infrared → Visible light → Ultraviolet → X-rays → Gamma rays (frequency increases, wavelength decreases in this order).

Give one source and one use each for X-rays and microwaves.

X-rays: produced by deceleration of high-energy electrons hitting a metal target; used in medical imaging and crystallography. Microwaves: produced by klystron/magnetron tubes; used in radar and microwave ovens/communication.

State the laws of reflection of light.

(1) The angle of incidence equals the angle of reflection (i = r). (2) The incident ray, reflected ray, and normal at the point of incidence all lie in the same plane.

State Snell's law of refraction and define refractive index.

Snell's law: n₁ sin i = n₂ sin r. The refractive index of a medium n = c/v = (speed of light in vacuum)/(speed in medium), also equal to sin i/sin r when light goes from vacuum to the medium.

Define critical angle and state the condition for total internal reflection.

The critical angle θ_c is the angle of incidence in the denser medium for which the angle of refraction is 90°: sinθ_c = 1/n. Total internal reflection occurs when light travels from a denser to rarer medium and the angle of incidence exceeds θ_c.

Write the lens maker's formula and the thin lens equation.

Lens maker's formula: 1/f = (n−1)(1/R₁ − 1/R₂). Thin lens equation: 1/v − 1/u = 1/f, where u, v are object and image distances and f the focal length.

Define the magnifying power of a compound microscope.

M = m_o × m_e = (L/f_o)(D/f_e), the product of the linear magnification of the objective and the angular magnification of the eyepiece, where L is tube length, D the least distance of distinct vision (25 cm), and f_o, f_e the focal lengths.

State the conditions for constructive and destructive interference of light.

Constructive (bright fringe): path difference = nλ (n = 0,1,2,...). Destructive (dark fringe): path difference = (n + ½)λ. Sources must be coherent.

Write the fringe width formula in Young's double-slit experiment.

β = λD/d, where λ is the wavelength, D the slit-to-screen distance, and d the separation between the slits.

What is the photoelectric effect and Einstein's photoelectric equation?

The photoelectric effect is the emission of electrons from a metal surface when light of suitable frequency falls on it. Einstein's equation: hν = φ + ½mv²_max, where hν is photon energy, φ the work function, and ½mv²_max the maximum kinetic energy of emitted electrons.

Define threshold frequency and work function.

Threshold frequency ν₀ is the minimum frequency of incident light below which no photoemission occurs. Work function φ = hν₀ is the minimum energy required to eject an electron from the metal surface.

State de Broglie's hypothesis and the wavelength of a matter wave.

Every moving particle has an associated wave. The de Broglie wavelength λ = h/p = h/mv, where h is Planck's constant, p the momentum. For an electron accelerated through V volts, λ ≈ 1.227/√V nm.

State the postulates of Bohr's model of the hydrogen atom.

(1) Electrons revolve in certain stable orbits without radiating energy. (2) Angular momentum is quantised: mvr = nh/2π. (3) Energy is emitted/absorbed only when an electron jumps between orbits: hν = E₂ − E₁.

Give the energy of the nth orbit of a hydrogen atom and the ground state energy.

Eₙ = −13.6/n² eV. The ground state (n=1) energy is −13.6 eV; the negative sign indicates the electron is bound.

Define mass defect and binding energy of a nucleus.

Mass defect Δm is the difference between the sum of masses of the constituent nucleons and the actual mass of the nucleus. Binding energy = Δm·c² is the energy needed to separate the nucleus into its nucleons (energy released when it forms).

Distinguish between nuclear fission and nuclear fusion.

Fission: a heavy nucleus splits into lighter nuclei releasing energy (e.g., U-235). Fusion: light nuclei combine to form a heavier nucleus releasing energy (e.g., in the Sun). Both release energy because products have higher binding energy per nucleon.

State the law of radioactive decay and define half-life.

The rate of decay is proportional to the number of undecayed nuclei: N = N₀e^(−λt), where λ is the decay constant. Half-life T₁/₂ = 0.693/λ is the time for half the nuclei to decay.

Distinguish between intrinsic and extrinsic semiconductors.

Intrinsic: pure semiconductor (e.g., pure Si/Ge) with equal numbers of electrons and holes. Extrinsic: doped with impurities to increase conductivity — n-type (pentavalent dopant, electrons majority) or p-type (trivalent dopant, holes majority).

What is a p-n junction diode and what is depletion region?

A p-n junction is formed by joining p-type and n-type semiconductors. The depletion region is the charge-free zone near the junction where diffused electrons and holes recombine, leaving immobile ions that set up a potential barrier.

Distinguish between forward bias and reverse bias of a diode.

Forward bias: p-side connected to positive terminal; barrier decreases, large current flows. Reverse bias: p-side to negative terminal; barrier increases, only a small reverse saturation current flows. A diode conducts mainly in forward bias.

What is the function of a Zener diode?

A Zener diode operates in the reverse breakdown region at a fixed voltage and is used as a voltage regulator, maintaining a constant output voltage despite changes in input voltage or load.

Describe the three regions of a transistor and the two types.

A transistor has three regions: emitter (heavily doped), base (thin, lightly doped), and collector (moderately doped, large). The two types are NPN and PNP, based on the arrangement of doped layers.

Define the current gain α and β of a transistor in common-base and common-emitter configurations.

α = I_C/I_E (common base, slightly less than 1). β = I_C/I_B (common emitter, large, ~20–200). They relate as β = α/(1−α).

How does a transistor act as an amplifier?

In active mode (emitter-base forward biased, collector-base reverse biased), a small change in base/input current produces a large change in collector/output current. A load resistor converts this into a larger output voltage, giving voltage gain (A_V = β × R_out/R_in).

What is the principle of a transformer and the turns ratio relation?

A transformer works on mutual induction: a changing current in the primary induces an EMF in the secondary. For an ideal transformer V_s/V_p = N_s/N_p = I_p/I_s, where N is the number of turns. Step-up has N_s > N_p; step-down has N_s < N_p.