Electricity

Electric current is the flow of electric charge through a conductor. It is measured as the rate of flow of charge, calculated by I = Q/t, where I is current in amperes, Q is charge in coulombs, and t is time in seconds. An ammeter is used to measure current in a circuit, connected in series.

Electric potential difference between two points is the work done to move a unit charge from one point to the other. It is calculated by V = W/Q, where V is potential difference in volts, W is work done in joules, and Q is charge in coulombs. A voltmeter measures potential difference, connected in parallel.

Ohm's Law states that the current through a conductor is directly proportional to the potential difference across its ends, provided temperature remains constant. It is expressed as V = IR, where V is potential difference, I is current, and R is resistance. This law helps in calculating unknown values in electric circuits.

Resistance of a conductor is calculated using R = ρl/A, where R is resistance, ρ is resistivity, l is length, and A is cross-sectional area. Resistivity depends on the material. For example, copper has lower resistivity than iron, making it a better conductor.

In series, resistors are connected end-to-end, and the same current flows through each. Total resistance is the sum of individual resistances (R_total = R1 + R2 + ...). In parallel, resistors are connected across the same two points, and voltage is the same across each. Total resistance is given by 1/R_total = 1/R1 + 1/R2 + ... .

Tungsten is used in electric bulbs because it has a high melting point (3380°C), allowing the filament to glow white-hot without melting. It also has high resistivity, which helps in converting electrical energy into light and heat efficiently. Additionally, tungsten's ductility makes it suitable for drawing into thin wires.

Heat produced is calculated using Joule's law: H = I²Rt. Here, I = 5 A, R = 20 Ω, t = 30 s. So, H = (5)² × 20 × 30 = 25 × 20 × 30 = 15000 J. This shows the energy dissipated as heat in the resistor.

The commercial unit of electrical energy is the kilowatt-hour (kWh). It is the energy consumed when 1 kW of power is used for 1 hour. 1 kWh = 1000 W × 3600 s = 3.6 × 10^6 J. This unit is used for billing electricity consumption.

Household appliances are connected in parallel so that each operates independently at the same voltage. If one appliance fails, others continue working. Parallel connection also allows drawing different currents as per appliance power ratings, unlike series where current is the same for all.

A fuse protects electrical circuits by breaking the circuit if current exceeds a safe value. It contains a wire that melts when overheated, stopping current flow. Fuses are rated by current (e.g., 5A, 10A) and prevent damage to appliances and fire hazards from overloading.

Resistance is directly proportional to length (R ∝ l) and inversely proportional to cross-sectional area (R ∝ 1/A). Doubling the length doubles resistance, while doubling the area halves resistance. This is derived from R = ρl/A, where ρ is resistivity.

Resistivity (ρ) is a material property that quantifies how strongly it opposes current flow. It depends on the material's nature and temperature but not on dimensions. For example, silver has the lowest resistivity (1.60 × 10^-8 Ωm), making it the best conductor among common materials.

Copper and aluminium are used for transmission due to their low resistivity, ensuring minimal energy loss as heat. They are also ductile (can be drawn into wires) and abundant. Aluminium is lighter and cheaper, often preferred for overhead lines despite slightly higher resistivity than copper.

First, find resistance using P = V²/R: R = V²/P = (220)²/100 = 484 Ω. At 110 V, power is P' = V'²/R = (110)²/484 = 25 W. Thus, power reduces to 25 W, showing that operating at half voltage reduces power to one-fourth.

The heating effect occurs when current flows through a resistor, converting electrical energy into heat (H = I²Rt). Applications include electric irons, heaters, toasters, and bulbs. In bulbs, a small part of heat is converted to light, while most appliances utilize the heat directly.

Series arrangement is unsuitable for domestic circuits because all appliances would share the same current, leading to inadequate operation if their power needs differ. A fault in one appliance would break the entire circuit. Parallel connection avoids these issues by providing independent operation.

Total resistance needed is R = V/I = 220/5 = 44 Ω. For parallel resistors, 1/R_total = n/R, where n is the number of resistors. So, 1/44 = n/176 → n = 176/44 = 4. Thus, four 176 Ω resistors in parallel are required.

In parallel, both bulbs operate at 220 V. The 100 W bulb consumes more power (100 J/s) than the 60 W bulb (60 J/s). Current drawn by 100 W bulb is I = P/V = 100/220 ≈ 0.45 A, and for 60 W bulb, I = 60/220 ≈ 0.27 A. Total current is 0.45 + 0.27 = 0.72 A.

(i) In series, R_total = R1 + R2 + R3 = 6 + 6 + 6 = 18 Ω. (ii) In parallel, 1/R_total = 1/R1 + 1/R2 + 1/R3 = 1/6 + 1/6 + 1/6 = 3/6 = 1/2 → R_total = 2 Ω. Thus, series gives higher resistance, parallel gives lower.

Alloys like nichrome have high resistivity and high melting points, making them suitable for heating elements. They do not oxidize easily at high temperatures, ensuring durability. Pure metals have low resistivity and would melt or oxidize quickly under similar conditions.

A voltmeter measures potential difference and is connected in parallel across the component. It has high resistance to avoid drawing significant current. An ammeter measures current and is connected in series. It has very low resistance to minimize voltage drop and not alter the circuit's current.

For most conductors, resistance increases with temperature. As temperature rises, atoms vibrate more, increasing collisions with electrons, which hinders their flow. This effect is quantified by the temperature coefficient of resistance, which is positive for metals like copper and aluminium.

The heating element is made of a high-resistance material (like nichrome) that heats up significantly due to I²R loss, glowing red-hot. The cord is made of low-resistance copper, which heats much less and does not glow, as its resistance is too low to produce visible heat at the same current.