Part I — MCQs (1 mark each)
1. Equipotential surfaces of a point charge are:
- (a) concentric spheres (b) planes (c) cylinders (d) cones
2. A wire of resistance 12 Ω is bent into a circle. The resistance between diametrically opposite points is:
- (a) 12 Ω (b) 3 Ω (c) 6 Ω (d) 24 Ω
3. The magnetic field inside a toroid depends on:
- (a) the material of the core (b) the radius of toroid (c) the current and number of turns (d) none
4. Self-inductance is analogous to which mechanical quantity?
- (a) Force (b) Velocity (c) Inertia (mass) (d) Displacement
5. In the EM spectrum, the frequency order from highest to lowest is:
- (a) γ rays > X-rays > UV > visible > IR > microwaves > radio
- (b) Radio > microwaves > IR > visible > UV > X-rays > γ rays
- (c) X-rays > γ rays > UV > visible
- (d) visible > UV > IR > X-rays
6. A convex lens of focal length 20 cm forms a real image at 60 cm from the lens. The object distance is:
- (a) 30 cm (b) 40 cm (c) 15 cm (d) 60 cm
7. The wavelength associated with an electron accelerated through 100 V is approximately:
- (a) 1.23 Å (b) 12.3 Å (c) 0.123 Å (d) 123 Å
8. An alpha particle is emitted from ²³⁸U₉₂. The resulting nucleus has:
- (a) Z=90, A=234 (b) Z=91, A=237 (c) Z=92, A=234 (d) Z=90, A=238
9. In a common emitter transistor, if β = 100 and base current = 20 μA, the collector current is:
- (a) 0.2 mA (b) 2 mA (c) 20 mA (d) 0.02 mA
10. The modulation index for FM is defined as:
- (a) carrier frequency / message frequency (b) frequency deviation / message frequency
- (c) message amplitude / carrier amplitude (d) carrier amplitude / message amplitude
11. For a resonating LCR series circuit, which is true?
- (a) XL > XC (b) XL < XC (c) XL = XC (d) R = 0
12. A Zener diode is used mainly for:
- (a) amplification (b) voltage regulation (c) rectification (d) modulation
13. The range of visible light wavelengths is:
- (a) 200–400 nm (b) 700–1000 nm (c) 400–700 nm (d) 1–10 nm
14. Davisson-Germer experiment confirmed:
- (a) particle nature of electrons (b) wave nature of electrons
- (c) wave nature of photons (d) photoelectric effect
15. The capacitance of a parallel plate capacitor filled with dielectric of constant k:
- (a) decreases by k (b) increases by k (c) remains same (d) decreases by k²
Part II — Very Short Answer (2 marks each)
1. What is electric flux? Write its SI unit. 2. State Ohm's Law. Give its limitations. 3. What is the principle of a transformer? 4. Why is the sky blue? Name the phenomenon. 5. Define binding energy. What is binding energy per nucleon for iron? 6. Define the β of a transistor. Write its relation to α.
Part III — Short Answer (3 marks each)
1. Derive the expression for electric field due to an infinite plane sheet of charge using Gauss's law. 2. Explain the working of a potentiometer to compare EMFs of two cells. 3. State Ampere's circuital law. Use it to find the field inside a solenoid. 4. Explain the construction and working of a full-wave bridge rectifier. 5. Using Bohr's model, derive the expression for the radius of the nth orbit of hydrogen atom. 6. Explain the photoelectric effect. What are the experimental laws governing it? 7. Explain n-type and p-type semiconductors with energy band diagrams. 8. Explain amplitude modulation with a block diagram. 9. Explain single slit diffraction. Find the width of the central maximum.
Part IV — Long Answer (5 marks each; internal choice)
Q1 (a): Define electric potential. Derive the expression for the electric potential due to a system of point charges. Show that potential is a scalar quantity and discuss equipotential surfaces.
OR
Q1 (b): Explain the parallel plate capacitor. Derive the expression for capacitance with and without a dielectric medium. Find the energy stored in a capacitor.
Q2 (a): Explain moving coil galvanometer — construction, working principle, and derivation of deflection formula. Explain how it is converted into an ammeter.
OR
Q2 (b): Derive an expression for the impedance and current in an LCR series circuit. Find the condition for resonance and Q-factor. Explain the power factor.
Q3 (a): Describe the construction and principle of a transformer. Derive the turns ratio formula. Describe losses in a transformer and how they are minimised.
OR
Q3 (b): Explain the common emitter transistor as an amplifier. Draw the circuit diagram. Derive the expression for voltage gain. Why is there a 180° phase shift?
Key Numerical Answers
- Visible light through lens: 1/f = 1/v − 1/u → 1/20 = 1/60 − 1/u → u = −30 cm
- de Broglie: λ = h/√(2meV) = 6.626×10⁻³⁴ / √(2×9.1×10⁻³¹×1.6×10⁻¹⁹×100) ≈ 1.23 Å
- Transistor: IC = β × IB = 100 × 20 × 10⁻⁶ = 2 × 10⁻³ A = 2 mA