8.4 Electricity & Magnetism

Why Electricity Matters for RRB Group D

Electricity is the most consistently tested physics topic in the RRB Group D exam. Expect 4–5 questions covering current and charge, Ohm's law, series/parallel circuits, electric power, the heating effect (electric iron, heater, fuse), and the magnetic effect of current. Candidates must be fluent with V = IR, P = VI, and the rules for combining resistors.

Electric Current and Charge

Electric current (I) is the rate of flow of electric charge through a conductor.

I = Q / t

SI unit: ampere (A), where 1 A = 1 C/s. The unit of charge is the coulomb (C); 1 C is the charge transported by a current of 1 A in 1 s. The charge on one electron is e = 1.6 × 10⁻¹⁹ C.

By convention, current flows from the positive terminal to the negative terminal of a cell, although electrons (negative charges) actually move from the negative terminal to the positive terminal.

Ohm's Law and Resistance

Ohm's law: At constant temperature, the current through a metallic conductor is directly proportional to the potential difference across its ends.

V = IR

where V is in volts, I in amperes, and R in ohms (Ω). 1 Ω is the resistance that allows 1 A of current when 1 V is applied.

Resistance and Resistivity

R = ρL / A

where ρ (rho) is the resistivity of the material (Ω·m), L is the length of the conductor (m), and A is its cross-sectional area (m²). Resistivity is a property of the material and depends on temperature, but not on the dimensions of the wire.

Conductors (metals) have very low resistivity; insulators (rubber, glass) have very high resistivity. Alloys such as manganin and nichrome are used in heating elements because they have higher resistivity than pure metals and do not oxidise easily at high temperatures.

Resistance of a metal increases with temperature; resistance of a semiconductor decreases with temperature.

Worked Example

A 2 m copper wire of cross-sectional area 1 × 10⁻⁶ m² has a resistivity of 1.7 × 10⁻⁸ Ω·m. Find its resistance.

R = ρL / A = (1.7 × 10⁻⁸ × 2) / (1 × 10⁻⁶) = 3.4 × 10⁻⁸ / 10⁻⁶ = 3.4 × 10⁻² Ω = 0.034 Ω.

Combination of Resistors

Series Combination

The same current flows through each resistor; the total voltage divides.

R_s = R₁ + R₂ + R₃ + …

Parallel Combination

The same voltage is applied across each resistor; the total current divides.

1/R_p = 1/R₁ + 1/R₂ + 1/R₃ + …

For two resistors in parallel: R_p = R₁R₂ / (R₁ + R₂).

Worked Example

Three resistors of 2 Ω, 3 Ω, and 6 Ω are connected in parallel. Find the equivalent resistance.

1/R_p = 1/2 + 1/3 + 1/6 = (3 + 2 + 1)/6 = 6/6 = 1.

So R_p = 1 Ω — much smaller than the smallest individual resistor, a hallmark of parallel circuits.

Electric Power and Energy

Power: P = VI = I²R = V²/R

SI unit: watt (W). The commercial unit of electrical energy is the kilowatt-hour (kWh), which is the energy consumed when a 1 kW appliance runs for 1 hour.

1 kWh = 3.6 × 10⁶ J.

Heating Effect of Current (Joule's Law)

When current passes through a conductor, the electrical energy is converted into heat: H = I²Rt (joules), or H = VIt / 4.18 (calories).

Applications: electric heater, electric iron, electric kettle, fuse. A fuse is a thin wire of low-melting-point alloy (tin-lead) that melts and breaks the circuit when the current exceeds a safe value, protecting the appliance.

Worked Example

A 100 W bulb is used for 5 hours a day for 30 days. If electricity costs ₹5 per kWh, find the bill.

Energy per day = 100 W × 5 h = 0.1 kW × 5 = 0.5 kWh. Energy for 30 days = 0.5 × 30 = 15 kWh. Bill = 15 × 5 = ₹75.

Magnetic Effects of Current

Magnetic Field Due to a Current

A current-carrying conductor produces a magnetic field around it. The right-hand thumb rule: if you hold the conductor in your right hand with the thumb pointing in the direction of the current, the curl of your fingers gives the direction of the magnetic field lines.

• A circular loop of current produces a field pattern like a small bar magnet.
• A solenoid (long coil of wire) produces a uniform field inside, like that of a bar magnet. A soft iron core inside a solenoid makes an electromagnet.

Force on a Current-Carrying Conductor in a Magnetic Field

A conductor carrying current in a magnetic field experiences a force (Fleming's left-hand rule): thumb = motion (force), forefinger = magnetic field, middle finger = current. This is the principle of an electric motor.

Electromagnetic Induction

When a conductor moves in a magnetic field such that it cuts the field lines, an induced current flows. Fleming's right-hand rule: thumb = motion, forefinger = field, middle finger = induced current. This is the principle of an electric generator.

Domestic Electric Circuits

Indian domestic supply is 220 V, 50 Hz AC. Circuits have a live wire (red/brown, at high potential), a neutral wire (black/blue, near ground potential), and a earth wire (green/yellow) that connects the metal body of an appliance to the earth, protecting the user from electric shock if a fault causes the body to become live.

A short circuit occurs when the live wire and neutral wire touch directly, causing a very large current that may blow the fuse. Overloading happens when too many appliances draw current beyond the safe limit of the wiring.