Electricity & Magnetism

Electric current (I): flow of electric charge. Unit: ampere (A). 1 A = 1 coulomb/second. By convention, current flows from + to − (opposite to actual electron flow).

Voltage / Potential difference (V): work done per unit charge to move it. Unit: volt (V). 1 V = 1 J/C. A battery maintains potential difference between its terminals.

Resistance (R): opposition to current flow. Unit: ohm (Ω). R = ρL/A (ρ = resistivity; L = length; A = cross-section). Long, thin wires of high-ρ material have high resistance.

Ohm's law: V = IR. Holds for metallic conductors at constant temperature.

Series combination: R_total = R₁ + R₂ + … Current is same through each. Voltage divides.
Parallel combination: 1/R_total = 1/R₁ + 1/R₂ + … Voltage is same across each. Current divides.

Power dissipated in a resistor: P = VI = I²R = V²/R. Unit: watt (W).

Energy = power × time. 1 unit of electricity = 1 kWh = 1000 × 3600 J = 3.6 × 10⁶ J.

Conductors and insulators:

• Good conductors: copper, aluminium, silver, iron.
• Insulators: rubber, plastic, glass, dry wood.
• Semiconductors: silicon, germanium (used in chips and transistors).
• Superconductors: zero resistance at very low temperatures.

Domestic wiring:

• Live wire (red/brown) carries current.
• Neutral wire (black/blue) completes circuit.
• Earth wire (green/yellow) provides safety path for fault currents.
• Fuses and circuit breakers prevent excess current.
• AC mains in India: 230 V at 50 Hz.

Magnetic effect of current (Oersted's discovery):

• Every current-carrying wire produces a magnetic field around it.
• Right-hand thumb rule: thumb points current direction → fingers curl in direction of magnetic field.
• A coil (solenoid) carrying current behaves like a bar magnet — used to make electromagnets.

Electromagnetic induction (Faraday's law): when magnetic flux through a coil changes, a current is induced in the coil. Basis of generators, transformers, induction stoves, MRI machines.

Example 1 — Ohm's law:
A 12 V battery is connected to a 4 Ω resistor. Current?
Method: I = V/R = 12/4 = 3 A.

Example 2 — Power:
A 60 W bulb on a 230 V supply. Current drawn?
Method: I = P/V = 60/230 ≈ 0.26 A.

Example 3 — Energy bill:
A 1.5 kW AC runs for 8 hours. Energy used?
Method: E = P × t = 1.5 × 8 = 12 kWh = 12 units. At ₹7/unit, cost = ₹84.

Example 4 — Parallel resistors:
Two resistors 6 Ω and 12 Ω in parallel. Equivalent resistance?
Method: 1/R = 1/6 + 1/12 = 3/12 = 1/4 → R = 4 Ω.

Example 5 — Series resistors:
Same two resistors in series: R = 6 + 12 = 18 Ω.

Household appliance facts:

• Geyser: 2000–3000 W, runs ~15 min/use.
• AC: 1500 W (1 ton ≈ 3500 BTU/h ≈ 1 kW input).
• Refrigerator: 100–250 W continuous.
• LED bulb: 9 W replaces a 60 W incandescent (six times more efficient).
• Iron: ~1000 W.
• Microwave: 800–1200 W.

Safety notes:

• Always switch off mains before fixing wiring.
• The earth wire protects you from shock if a metal appliance casing becomes live.
• A fuse melts and breaks the circuit if current exceeds its rating.
• An MCB (Miniature Circuit Breaker) does the same job but is resettable.
• Lightning rods conduct lightning to the ground safely.

Magnetism facts:

• Earth itself is a giant magnet — North magnetic pole is in the Arctic (actually slightly south of geographic North).
• A compass needle aligns with Earth's magnetic field, pointing roughly north–south.
• The Curie temperature is the temperature above which a magnetic material loses its magnetism (iron ~770°C).
• Magnetic Resonance Imaging (MRI) uses strong magnetic fields to image internal organs.