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UNIT 1: Rotational Dynamics & Oscillations
Q1. Explain moment of inertia of the rigid body and torque. Also find the rotational kinetic energy of rigid body and condition of conservation.
- Moment of Inertia (I): Rotational analogue of mass. Measures resistance to rotational motion. I = Σ m_i * r_i^2
- Torque (τ): Turning effect of force. τ = I * α = r × F
- Rotational Kinetic Energy: Derivation clue for a rotating body with angular velocity ω:
K.E._rot = 0.5 * I * ω^2
- Conservation of Angular Momentum: Under zero external torque (τ = 0), angular momentum remains constant.
L = I * ω = Constant
Q2. Set up differential equation of an oscillation of horizontal spring by application of Hook’s law and Newton’s law. Write it’s solution. Also find acceleration, time period and velocity.
- Differential Equation Setup: Combining F = -kx and F = m(d^2x/dt^2):
d^2x/dt^2 + (k/m)x = 0 => d^2x/dt^2 + ω^2*x = 0
- General Solution: x(t) = A * cos(ωt + φ)
- Velocity (v): v = dx/dt = ±ω √(A^2 - x^2)
- Acceleration (a): a = dv/dt = -ω^2 * x
- Time Period (T): T = 2π / ω = 2π √(m/k)
UNIT 2: Magnetic Fields & Material Properties
Q3. Discuss magnetic dipole moment. What is its effect on atom and on molecules? Explain.
- Magnetic Dipole Moment (μ): For a loop, μ = I * A. In atoms, it arises from electron orbit and electron spin.
- Effects: Organizes materials into Diamagnetic (no permanent moment), Paramagnetic (random permanent moments aligned by external field), and Ferromagnetic (strong domain alignment).
Q4. Discuss Hall Effect.
- Concept: Generation of a transverse voltage (Hall voltage) across a current-carrying conductor when placed in a perpendicular magnetic field.
- Formula Clue:
V_H = (I * B) / (n * e * t)
- Application: Used to calculate carrier concentration (n) and identify carrier type (n-type or p-type).
Q5. Torque on rectangular coil.
- When a current-carrying loop of area A is placed in a magnetic field B, it experiences a rotational torque:
τ = N * I * A * B * sin(θ)
UNIT 3: Quantum Mechanics & Atomic Physics
Q6. What is black body and black body radiation? Explain the characteristics of black body radiation.
- Black Body: An ideal surface that absorbs 100% of incident radiation.
- Characteristics: Continuous spectrum, energy density increases with temperature, and peak wavelength shifts down as temperature goes up (Wien's Law: λ_max * T = constant).
Q7. State Franck-Hertz experiment and explain his experiment.
- Purpose: Proved the existence of discrete, quantized energy states in atoms.
- Mechanism: Passing electrons through mercury vapor showed periodic drops in current at specific accelerating voltages (multiples of 4.9V), demonstrating inelastic collisions at exact energy thresholds.
Q8. State Uncertainty Principle.
- It is impossible to measure both the exact position and exact momentum of a subatomic particle simultaneously.
Δx * Δp ≥ h-bar / 2
UNIT 4: Schrodinger Equation & Hydrogen Atom
Q9. Set up Schrodinger equation for hydrogen atom using spherical polar co-ordinates out separate radical and angular part of this equation without solving angular and radical-equation. Discuss the quantum number associated with these.
- Setup Hint: Express ∇^2 in spherical coordinates (r, θ, φ) with potential V = -e^2 / (4πε_0*r).
- Separation: Assume wavefunction solution ψ(r, θ, φ) = R(r) * Θ(θ) * Φ(φ) to isolate variables.
- Quantum Numbers:
- Principal Quantum Number (n) → From Radial Part
- Orbital Quantum Number (l) → From Angular Part
- Magnetic Quantum Number (m_l) → From Angular Part (φ)
UNIT 5: Band Theory of Solids
Q10. Discuss effective mass of electron and holes.
- Electrons moving inside a periodic crystal lattice behave as if they have a modified mass due to internal forces.
m* = (h-bar)^2 / (d^2E / dk^2)
- Positive curvature near conduction band bottom = positive mass; negative curvature near valence band top = negative mass (treated as positive holes).
Q11. Discuss Kronig-Penny Model.
- An idealized 1D model using periodic square-well potentials to describe electron states in a crystal lattice.
- Outcome: Validates the generation of allowed energy bands and forbidden energy gaps (Eg) using Bloch's theorem.
UNIT 6: Semiconductors & Junction Devices
Q12. Carrier concentration of Intrinsic Semiconductor also find the Eg=(Ec + Ev)/2 where symbols have usual meanings
- By equating electron concentration (n) and hole concentration (p):
N_c * exp(-(E_c - E_f)/kT) = N_v * exp(-(E_f - E_v)/kT)
- Assuming N_c ≈ N_v and isolating E_f yields the middle point of the band gap:
E_f = (E_c + E_v) / 2
Q13. Explain equilibrium current across the P-N junction. Use Fermi-Dirac statistics and Maxwell Boltzmann distribution to show flow N to P is equal to the flow P to N. How electron current from P to N is not affected by the height of the potential energy barrier? Explain.
- At equilibrium, diffusion current balances drift current (Net current = 0).
- High-energy tails match Maxwell-Boltzmann distributions, regulating carrier balance over the barrier.
- Crucial point: P to N current is a minority carrier drift current. It depends strictly on thermal generation of carriers on the P-side, not on the barrier height, because the internal electric field sweeps any available minority carrier across immediately regardless of barrier size.
Q14. Explain the construction and working of bipolar junction transistor (BJT).
- Structure: Three layers — Emitter (heavily doped), Base (thin, lightly doped), and Collector (moderately doped). Configurations: NPN and PNP.
- Operation: In active mode, the Emitter-Base is forward biased to inject carriers, and the Collector-Base is reverse biased to extract them. KCL balance: I_E = I_B + I_C.
UNIT 7: Digital Electronics & IC Fabrication
Q15. Explain RTL and TTL gates. How memory and clock circuits can be made by using these gates? Explain how they work?
- RTL: Resistor-Transistor Logic. Uses resistors at inputs and BJTs for switching logic.
- TTL: Transistor-Transistor Logic. Uses multi-emitter transistors at inputs for improved speed.
- Memory: Cross-coupling NAND/NOR configurations sets up a feedback loop to create latch flip-flops.
- Clocks: Adding Resistor-Capacitor (RC) time-delay loops inside the cross-coupled feedback system yields astable multi-vibrators that alternate states periodically.
Q16. Describe the following process of IC production: a)Oxidation b)Pattern definition and c) Doping.
- a) Oxidation: Thermal growth of protective, insulating Silicon Dioxide (SiO2) layers at high heat using oxygen gas or steam.
- b) Pattern Definition (Photolithography): Masking, applying UV light sensitive photoresist, and chemical etching to print spatial microcircuit geometric configurations onto the wafer.
- c) Doping: Selectively introducing specialized trivalent/pentavalent impurities using high-temp thermal diffusion or high-energy ion implantation to establish localized P or N zones.
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