Ohm's Law: The current (I) through a conductor is directly proportional to the potential difference (V) across it at constant temperature. V = IR, where R = resistance (Ω). Not all materials obey Ohm's Law (diodes, thermistors are non-ohmic).

Class 12 Science Exercise Solutions

Class 12 Science — Exercise Solutions

This section covers the key topics in Class 12 Science: Electrostatics, Current Electricity, Magnetism, Electromagnetic Induction, and Optics.

I. Electrostatics

Q1. State Coulomb's Law. F = kq₁q₂/r² (k = 9×10⁹ Nm²C⁻²). Force between two charges is proportional to product of charges and inversely proportional to square of distance.

Q2. What is electric potential? Electric potential (V) at a point = work done per unit positive charge in bringing a test charge from infinity to that point. V = W/q. Unit: Volt (V). Relation to field: E = −dV/dr.

Q3. What is capacitance? Capacitance C = Q/V (Farads). For parallel plate capacitor: C = ε₀A/d. Energy stored = ½CV².

II. Current Electricity

Q1. State Ohm's Law and its limitations. V = IR. Limitations: not applicable to diodes, transistors, electrolytes, vacuum tubes.

Q2. What is resistivity? Resistivity (ρ): R = ρL/A. Unit: Ω·m. For metals, ρ increases with temperature. For semiconductors, ρ decreases with temperature.

Q3. Kirchhoff's Laws:

Answer

KCL: sum of currents at junction = 0.
KVL: sum of EMF = sum of IR drops in closed loop.

III. Magnetism

Q1. What is the force on a current-carrying conductor in a magnetic field? F = BIL sinθ. Maximum when θ = 90° (conductor perpendicular to B). F = BIL.

Q2. What is the Biot-Savart Law? dB = (μ₀/4π)(I dl × r̂)/r². Magnetic field due to small current element. μ₀ = 4π×10⁻⁷ T·m/A.

IV. Electromagnetic Induction

Q1. State Faraday's Laws of Electromagnetic Induction. 1st Law: EMF is induced in a conductor when there is a change in magnetic flux. 2nd Law: Magnitude of induced EMF = rate of change of flux: ε = −dΦ/dt.

Q2. What is Lenz's Law? The induced current opposes the change in flux that produces it (conservation of energy).

Q3. What is a transformer? V₁/V₂ = N₁/N₂ = I₂/I₁. Step-up: N₂ > N₁. Based on mutual induction.

V. Optics and Wave Optics

Q1. State Snell's Law of Refraction. n₁ sin θ₁ = n₂ sin θ₂. Light bends towards normal when entering denser medium.

Q2. What is total internal reflection? When light goes from denser to rarer medium at angle ≥ critical angle (sin c = 1/n). Applications: optical fibres, prisms, diamonds.

Q3. What are the conditions for constructive and destructive interference? Constructive: path difference = nλ (bright fringe). Destructive: path difference = (n+½)λ (dark fringe). Fringe width β = λD/d (D = screen distance, d = slit separation).

Exam Checklist

Coulomb's Law: F = kq₁q₂/r²; k = 9×10⁹.
Capacitor: C = ε₀A/d; energy = ½CV².
Ohm's Law: V = IR; resistivity R = ρL/A.
Faraday: ε = −dΦ/dt; Lenz's Law: opposes change.
Transformer: V₁/V₂ = N₁/N₂.
Snell's Law: n₁sinθ₁ = n₂sinθ₂.
Young's double slit: β = λD/d.

Frequently Asked Questions

Coulomb's Law: The electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. F = kq₁q₂/r² where k = 9×10⁹ Nm²C⁻². Like charges repel; unlike charges attract.