Electricity

Electric charge is the basic property of matter that gives rise to all electrical effects, and it comes in two kinds.

• There are two kinds of charge — positive (+) and negative (−).
• Like charges repel and unlike charges attract each other.
• The SI unit of charge is the coulomb (C).
• Charge is quantised: it occurs in whole multiples of the electronic charge e = 1.6 × 10⁻¹⁹ C.
• Charge is conserved — it can neither be created nor destroyed, only transferred.
• A body becomes positively charged by losing electrons and negatively charged by gaining electrons.

Materials are divided by how freely they allow charge to pass through them.

• Insulators do not allow current to pass through them — they have almost no free electrons.
• Metals like silver, copper and aluminium are good conductors; silver is the best conductor.
• Rubber, glass, wood, plastic and dry air are good insulators.
• The human body, earth and impure water are conductors of electricity.

Charge at rest produces static electricity, and the force between two charges follows a simple inverse-square law.

• It is produced by friction — e.g. rubbing a glass rod with silk or a comb through dry hair.
• A charged comb attracts tiny bits of paper because of the static charge on it.
• Lightning is a large-scale natural discharge of static electricity.

• The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
• F = k·q₁·q₂ / r² — where q₁, q₂ are the charges, r is the distance, and k = 9 × 10⁹ N·m²/C².
• The force acts along the line joining the two charges.

When charge flows through a conductor, we call it an electric current, and its strength is the rate at which charge passes a point.

• I = Q / t — Current = Charge ÷ Time, where Q is charge in coulomb and t is time in second.
• The SI unit of current is the ampere (A).
• 1 ampere = 1 coulomb per second (1 A = 1 C/s).
• Current is measured by an ammeter, which is connected in series in the circuit.
• Current is a scalar quantity (it has magnitude but no direction in the vector sense).

• Conventional current flows from the positive (+) terminal to the negative (−) terminal of a cell, outside it.
• Electrons actually flow from negative (−) to positive (+) — opposite to the conventional current.
• So conventional current direction is opposite to the direction of electron flow.

To push current through a circuit there must be a difference in electrical "pressure" between two points, and this is the potential difference or voltage.

• V = W / Q — Voltage = Work ÷ Charge.
• The SI unit of potential difference is the volt (V).
• 1 volt = 1 joule per coulomb (1 V = 1 J/C).
• Potential difference is measured by a voltmeter, which is connected in parallel across the two points.
• A cell or battery provides the potential difference that drives current through a circuit.

Ohm's law is the central rule of simple circuits, linking voltage, current and resistance.

• V ∝ I, so V = IR — where V is voltage, I is current and R is resistance.
• R = V / I and I = V / R — the three rearranged forms.
• The law holds only at constant temperature (and for "ohmic" conductors like metals).
• Given by German physicist Georg Simon Ohm.

Resistance is the opposition a conductor offers to the flow of current, and it depends on the conductor's shape, material and temperature.

• The SI unit of resistance is the ohm (Ω).
• 1 ohm = 1 volt per ampere (1 Ω = 1 V/A).
• Good conductors have low resistance; insulators have very high resistance.

• Resistance increases with the length of the conductor — R ∝ L (longer wire = more resistance).
• Resistance decreases as the area of cross-section increases — R ∝ 1/A (thicker wire = less resistance).
• Resistance depends on the material of the conductor.
• Resistance increases with temperature for metals (hotter wire = more resistance).

Resistivity is the property of the material itself, independent of the size or shape of the wire.

• Resistivity ρ depends only on the material and its temperature, not on the wire's dimensions.
• The SI unit of resistivity is the ohm-metre (Ω·m).
• Metals have low resistivity; insulators have very high resistivity.
• Silver has the lowest resistivity and is the best conductor; alloys like nichrome have high resistivity, so they are used in heating elements.

Resistances (or appliances) can be joined end-to-end in series or side-by-side in parallel, and the two arrangements behave very differently.

• The same current flows through every component.
• The total resistance is the sum: R = R₁ + R₂ + R₃ — resistance increases.
• If one component fails, the whole circuit breaks (like old fairy lights).
• Voltage is divided among the components.

• In parallel, components are joined across the same two points on separate branches.
• The voltage is the same across every branch.
• Total resistance is given by 1/R = 1/R₁ + 1/R₂ + 1/R₃ — resistance decreases (less than the smallest).
• If one branch fails, the others keep working.
• Current is divided among the branches.
• Household wiring uses parallel connection so each appliance gets the full mains voltage and works independently.

Electric power is the rate at which electrical energy is used or supplied, and it can be written in three handy forms.

• P = V × I — Power = Voltage × Current.
• Using Ohm's law, also P = I² × R and P = V² / R.
• The SI unit of power is the watt (W).
• 1 watt = 1 joule per second (1 W = 1 J/s) and 1 W = 1 volt × 1 ampere.
• 1 kilowatt (kW) = 1000 watt and 1 horsepower (HP) = 746 W.
• The power rating of a bulb (e.g. 60 W, 100 W) tells how much energy it uses per second.

When current flows through a resistor it produces heat, and this heating effect powers many everyday appliances.

• H = I² × R × t (Joule's law of heating) — where H is heat, I is current, R is resistance and t is time.
• Heat produced is proportional to the square of the current (H ∝ I²), to resistance, and to time.

• Electric bulb — a thin tungsten filament glows white-hot and gives light (tungsten has a very high melting point).
• Electric heater, iron, geyser, toaster and oven — use a high-resistance nichrome coil to produce heat.
• Electric fuse — a thin wire that melts when too much current flows, protecting the circuit.
• Filaments are made of tungsten and heating elements of nichrome because both have high melting points and high resistance.

The fuse is the simplest safety device in a circuit, designed to break the circuit before the wiring can overheat.

• It is a short, thin wire of high-resistance, low-melting-point alloy (tin–lead).
• When the current exceeds a safe limit, the fuse wire heats up and melts, breaking the circuit.
• A fuse is always connected in series with the live (phase) wire.
• It guards against short circuits and overloading, which can otherwise cause fires.
• Modern homes also use an MCB (Miniature Circuit Breaker) as a reusable alternative to the fuse.

Electricity bills are not charged in joules but in a larger, practical unit suited to household use.

• 1 kWh = 1 unit of electricity — this is what appears on the electricity bill.
• 1 kWh = energy used by a 1 kW appliance running for 1 hour.
• 1 kWh = 3.6 × 10⁶ J = 3,600,000 joule.
• Energy (in kWh) = Power (in kW) × Time (in hours).
• The SI unit of energy is the joule (J), but it is too small for billing, so the kWh is used.

Home electricity reaches us through three wires, each colour-coded and each with a specific safety role.

• Neutral wire — completes the circuit at low (zero) potential; usually black or blue.
• Earth (Ground) wire — a safety wire connected to the metal body of appliances; usually green.
• In India the household supply is 220–230 V AC at 50 Hz.

• The earth wire protects against electric shock by safely passing any leakage current to the ground.
• The fuse and switch are always placed in the live wire.
• Overloading and short circuits are the main causes of electrical fires.
• Appliances are connected in parallel so each receives the full 220 V and runs independently.

A current and a magnet are deeply linked, but the details belong to a separate chapter.

• A changing magnetic field produces a current — electromagnetic induction (Faraday).
• Electric motors, generators and transformers all use this current–magnet relationship.
• The full topic of electromagnetism is covered in the Magnetism chapter.