12th Physics SLO Based Guess
PHYSICS 12th Federal Board
(20 MOST IMPORTANT TOPICS)
To watch Details Explanation of each topic: Click Here
SLO Based Topic Questions are:
Explain Gauss’s law and calculate electric field for infinite sheet of charges?
· State Gauss’s law mathematically and explain the concept.
· Choose a Gaussian surface (cylinder perpendicular to the sheet).
· Justify symmetry and field direction.
· Apply Gauss’s Law: Φ_E = E · A = q_enc/ε₀.
· Calculate E = σ/(2ε₀).
· Box the final expression.
How Gauss’s law can be used to find electric field between oppositely charged parallel plates?
· Consider two parallel sheets with +σ and -σ.
· Use superposition of fields: inside adds, outside cancels.
· Derive: E = σ/ε₀.
· Use a diagram to show field lines.
What is equipotential surface?
· Define: surface of constant potential.
· State: no work done in moving charge.
· Sketch equipotentials around point/line charges.
Describe the effect of potential on equipotential surfaces?
· Discuss electric field direction: ⊥ to equipotential.
· Closer lines → stronger field.
· Relate gradient of potential to field: E = -dV/dx.
Derive the electron volt relation with joule?
· Define electron volt.
· Use W = qV → 1eV = 1.6 × 10⁻¹⁹ J.
· State use in atomic/nuclear scales.
Explain how electron volt is different from potential difference?
· Define both terms.
· Emphasize: eV is energy; potential is cause of energy gain.
· Give example: energy of 1 electron at 5V is 5 eV.
Explain the factors affecting the capacitance of capacitor?
· Write capacitance formula: C = ε₀ε_rA/d.
· Explain effects of each variable.
· Add examples or a table.
Calculate the energy stored in a capacitor?
· Use W = ∫₀^Q V dq.
· Substitute V = q/C.
· Integrate and simplify to get U = ½CV².
Calculate the current and voltage across each resistor in given circuit?
· Redraw the circuit clearly.
· Identify series/parallel combinations.
· Find equivalent resistance.
· Apply Ohm’s law: V = IR.
· Use current/voltage division rules.
What is the principle of Wheatstone bridge?
· Draw the circuit.
· State balancing condition: no current in galvanometer.
· Derive R₁/R₂ = R₃/Rx.
Calculate the unknown resistance of a circuit by Wheatstone bridge?
· Use balance condition.
· Rearrange to solve for unknown: Rx = (R₃·R₂)/R₁.
· Include unit and final boxed answer.
Explain the relationship of potentiometer with the help of diagram?
· Draw a standard potentiometer setup.
· Explain principle: V ∝ L.
· Describe null point method.
· Derive ratio E₁/E₂ = L₁/L₂.
What are the applications of potentiometer?
· List with brief explanation:
· - EMF comparison.
· - Find internal resistance.
· - Calibration.
· Use small sketches or flowcharts if possible.
Derive the relation for maximum power output of any circuit?
· Start with P = I²R, I = E/(R + r).
· Substitute into power formula.
· Differentiate P w.r.t R, set dP/dR = 0.
· Get R = r; max power P = E²/(4r).
Explain Faraday’s law and how it is related with Lenz’s law?
· Write Faraday’s law: ε = -dΦ/dt.
· Explain sign: Lenz’s law.
· Give example: magnet in coil.
Does Lenz’s law violate law of conservation of energy?
· Explain induced current opposes change.
· Work is done against opposing force.
· Energy is conserved, not created.
Describe Ampere’s Law and calculate the magnetic field for solenoid?
· State law: ∮B·dl = μ₀I_enc.
· Use rectangle loop inside solenoid.
· Derive B = μ₀nI.
Derive the relationship for emf generated by AC generator?
· Use flux: Φ = NBA cos(ωt).
· Differentiate: ε = -dΦ/dt = NABω sin(ωt).
Explain impedance, current/voltage and derive its relation of RLC series circuit?
· Draw RLC circuit.
· Impedance: Z = √(R² + (X_L - X_C)²).
· Write current: I = V/Z.
· Phase angle: tanφ = (X_L - X_C)/R.
Derive the relations of Maxwell Equations?
· Write four equations in differential form.
· Explain each:
· - Gauss’s law (E, B).
· - Faraday’s law.
· - Ampere-Maxwell law.
· Mention wave implications.
Explain the process of half wave rectification and explain the working of it?
· Draw circuit.
· Explain diode behavior.
· Show output graph.
· Mention only positive half passes.
How full wave rectifier can be used to convert AC source into DC output?
· Draw bridge rectifier.
· Show current path in both cycles.
· Output: full-wave DC.
· Add waveform graph.
Explain the type of configurations in transistors?
· List: CB, CE, CC.
· Draw circuit for each.
· State input/output resistance and gains.
Describe the applications of both Common-Base and Common-Emitter Transistor?
· CB: Voltage amplification, RF circuits.
· CE: General amplifier, large gain.
· Compare in a table.
Explain the types of materials according to energy band theory?
· Draw band diagrams.
· Explain energy gap:
· - Conductor: 0 gap.
· - Insulator: >5 eV.
· - Semiconductor: ~1 eV.
Discuss the types of magnetic materials and explain their examples?
· Define: Dia, Para, Ferro.
· Describe alignment of domains.
· Give examples and graphs.
Explain the postulates of special theory of relativity with the help of examples?
· State two postulates.
· Give example: light speed from moving train same in all frames.
Explain any three consequences of special theory of relativity?
· Time dilation: t = t₀ / √(1 - v²/c²).
· Length contraction: L = L₀ √(1 - v²/c²).
· Mass-energy: E = mc².
Explain the photo electric effect and how it verifies the particle nature of light?
· Describe experiment.
· Observations: threshold freq, instant emission.
· Einstein’s equation: E = hν = φ + KE.
· Proves photons.
Briefly explain the concept of photon?
· Energy quantization: E = hν.
· Light as particles: packets of energy.
· Related to photoelectric effect.
Deduce the relation of De Broglie Wavelength?
· Start with p = mv.
· Use λ = h/p.
· Apply to electrons, verify wave nature.
Discuss the half-life of radioactive elements and derive the relation to calculate it?
· Start with decay law: N = N₀ e^(-λt).
· At half-life: N = N₀/2.
· Derive T₁/₂ = 0.693/λ.
08 Conceptual Questions:
1. Water has a large dielectric constant but rarely used in capacitors. Why?
Water has a high dielectric constant, which should be ideal for capacitors. However, it is a polar solvent and conducts electricity due to dissolved ions, causing leakage currents or dielectric breakdown. Formula: C = ε₀A/d.
2. Under what circumstances can terminal P.D. of a battery exceeds EMF?
The terminal voltage of a battery is V = ε - Ir during discharge, and V = ε + Ir during charging. So during external charging, terminal voltage can exceed the EMF. Example: A 12V battery being charged at 2A with r = 1Ω gives V = 14V.
3. If a current passes through an unstretched spring, will it contract or expand?
A current in a helical spring creates a magnetic field along its axis. The Lorentz force causes the coils to attract each other, leading to contraction. Formula: Force per unit length F = μ₀I²/2πr. Example: Used in magnetic actuators.
4. How Eddy current can be minimized in transformer?
Eddy currents are loops of induced current in conductors due to changing magnetic fields. To minimize them, transformer cores are laminated, reducing area for loops. Formula: Power loss P = I²R. Example: Iron cores are laminated to reduce heating.
5. How does doubling the frequency affect the reactance of (a) inductor (b) capacitor?
(a) Inductive reactance XL = 2πfL: doubling f doubles XL. (b) Capacitive reactance XC = 1/2πfC: doubling f halves XC. Example: In AC circuits, frequency shift alters current flow significantly.
6. What is the difference between Elastic deformation and plastic deformation?
Elastic deformation is temporary and follows Hooke’s Law: F = kx. Plastic deformation is permanent and occurs beyond yield strength. Example: A stretched rubber band is elastic; bent metal beyond limit is plastic.
7. Distinguish between Soft and Hard substances by drawing its curves?
Stress–strain curves: Soft materials show shallow slope, low yield point. Hard materials have steep slope, high stress before yielding. Example: Lead is soft; steel is hard and resists deformation.
8. Why don't we observe the Compton's effect with visible light?
Compton shift: Δλ = (h/m(e)c)(1 - cosθ). For visible light (λ ~ 500 nm), shift is negligible. Example: X-rays show measurable shift; visible light does not.
05 Numerical Chapters:
1. A 280 J of work is done in carrying a charge of 2 C from a place where the potential is -12 V to another place where the potential is V. Calculate the value of V?
Step 1: Use the relation W = q(V - Vi)
Step 2: Rearranging gives V = W/q + Vi
Step 3: Substitute values: V = 280 / 2 + (-12) = 140 - 12
Final Answer: V = 128 V
2. Two-point charges of 8 μC and -4 μC are separated by 10 m. At what point on the line joining them is the electric potential zero?
Step 1: Let distance from +8μC charge to point be x.
Step 2: Set potentials equal: 8/x = 4/(10 - x)
Step 3: Solve: 8(10 - x) = 4x => 80 - 8x = 4x => 12x = 80 => x = 6.67 m
Final Answer: 6.67 m from +8 μC charge
3. A 6 μF capacitor is charged to 120 V and connected to an uncharged 4 μF capacitor. Calculate the new P.D.
Step 1: Find total charge: Q = C × V = 6μF × 120V = 720 μC
Step 2: Total capacitance = 6 + 4 = 10 μF
Step 3: V = Q / C = 720 / 10 = 72 V
Final Answer: 72 V
4. A carbon electrode has resistance 0.125 Ω at 20°C. α = -0.0005/°C. Find resistance at 85°C.
Step 1: ΔT = 85 - 20 = 65°C
Step 2: R = R0(1 + αΔT) = 0.125(1 - 0.0005 × 65)
Step 3: R = 0.125(0.9675) = 0.1209 Ω
Final Answer: 0.1209 Ω
5. A 10 W resistor has resistance 120 Ω. Find the current.
Step 1: Use P = I²R ⇒ I = √(P/R)
Step 2: I = √(10 / 120) = √0.0833 = 0.289 A
Final Answer: 0.289 A
6. A 50 Ω resistor has 100 V across it for 1 hour. Calculate (a) Power (b) Energy.
Step 1: P = V² / R = 100² / 50 = 200 W
Step 2: E = P × t = 200 × 3600 = 720,000 J
Final Answer: (a) 200 W, (b) 720,000 J
7. Find distance from wire with 10 A current where B = 5×10⁻⁴ T.
Step 1: B = μ₀I / (2πr) ⇒ r = μ₀I / (2πB)
Step 2: r = (4π×10⁻⁷×10) / (2π×5×10⁻⁴) = 4×10⁻³ m
Final Answer: 4 mm
8. An 8 MeV proton enters 2.5 T field perpendicularly. Find force and radius.
Step 1: Convert E to joules: 8 MeV = 1.28×10⁻¹² J
Step 2: v = √(2E/m) = √(2×1.28×10⁻¹² / 1.67×10⁻²⁷)
Step 3: F = evB = 1.6×10⁻¹⁹ × v × 2.5 = 1.57×10⁻¹¹ N
Step 4: r = mv / (eB) = 0.163 m
Final Answer: (a) 1.57×10⁻¹¹ N, (b) 0.163 m
9. Coil with 250 turns, 6 cm × 4 cm, max torque 0.20 Nm in 0.25 T. Find current.
Step 1: A = 0.06 × 0.04 = 0.0024 m²
Step 2: τ = NIBA ⇒ I = τ / (NBA) = 0.20 / (250 × 0.25 × 0.0024)
Final Answer: 1.33 A
10. Two wires 10 cm apart carry 8 A opposite directions. Find B halfway.
Step 1: B = μ₀I / (2πr), r = 0.05 m (halfway)
Step 2: B_total = 2 × (μ₀I / 2πr) = μ₀I / πr = 6.4×10⁻⁵ T
Final Answer: 6.4×10⁻⁵ T
11. Length appears 1/3rd. Find speed.
Step 1: L = L₀√(1 - v²/c²) ⇒ 1/3 = √(1 - v²/c²)
Step 2: Square both sides: 1/9 = 1 - v²/c² ⇒ v²/c² = 8/9 ⇒ v = c√(8/9)
Step 3: v = 3×10⁸ × √(8/9) = 2.83×10⁸ m/s
Final Answer: 2.83×10⁸ m/s
12. 50 keV X-ray scattered 90°. Find energy after scattering.
Step 1: Δλ = h/(mec)(1 - cosθ) = 0.00243 nm
Step 2: E' = hc / (λ + Δλ) ⇒ E' ≈ 45.56 keV
Final Answer: 45.56 keV
13. Mass of 14N = 13.999234 u. Find binding energy.
Step 1: Mass of parts = 7p + 7n = 7(1.007276) + 7(1.008665) = 14.1115 u
Step 2: Mass defect = 14.1115 - 13.999234 = 0.1123 u
Step 3: BE = Δm × 931.5 = 104.66 MeV
Final Answer: 104.66 MeV
14. Half-life of Ra = 1.6×10³ years. Find decay constant.
Step 1: λ = ln(2)/T₁/₂ = 0.693 / (1.6×10³ × 365 × 24 × 3600)
Step 2: λ = 1.37×10⁻¹¹ s⁻¹
Final Answer: 1.37×10⁻¹¹ s⁻¹
15. Th → Pa β-decay. Mass Th = 234.0436 u, Pa = 234.0428 u. Find energy released.
Step 1: Δm = 234.0436 - 234.0428 = 0.0008 u
Step 2: E = Δm × 931.5 = 0.0008 × 931.5 = 0.745 MeV
Final Answer: 0.745 MeV
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