Electric charge: property of matter that causes electrical phenomena. Two types: positive (proton) and negative (electron). Like charges repel; unlike charges attract. SI unit: Coulomb (C). Electric current: rate of flow of electric charge. I = Q/t. SI unit: Ampere (A). 1 A = 1 C/s. Current flows from positive to negative terminal in external circuit (conventional); electrons actually flow opposite. Measured by ammeter (connected in series). Potential difference (voltage): work done per unit charge to move charge between two points. V = W/Q. SI unit: Volt (V). Measured by voltmeter (connected in parallel).

Ohm's Law: At constant temperature, the current through a conductor is directly proportional to the potential difference across it. V = IR (V = voltage, I = current, R = resistance). Resistance (R): opposition to current flow. SI unit: Ohm (Ω). 1 Ω = 1 V/A. Resistance depends on: length (R ∝ L), cross-sectional area (R ∝ 1/A), material (resistivity ρ), temperature (R increases with temperature for metals). Formula: R = ρL/A. Resistivity (ρ) is a material property. Good conductors (copper, aluminium) have low resistivity; insulators (rubber, glass) have very high resistivity.

Series combination: resistors connected end-to-end. Same current flows through all. Total resistance: R_s = R₁ + R₂ + R₃. Voltage divides across resistors. If one component fails, circuit breaks. Parallel combination: resistors connected between same two points. Same voltage across all. Total resistance: 1/R_p = 1/R₁ + 1/R₂ + 1/R₃. R_p is always less than smallest individual resistor. Current divides. One component failing does not affect others (used in household wiring). Domestic circuits: parallel connection used so each appliance gets full 220V and can be switched independently.

Electric power: rate of doing electrical work. P = VI = I²R = V²/R. SI unit: Watt (W). 1 W = 1 J/s. Commercial unit of energy: kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J = 1 unit of electricity. Heating effect of current (Joule's Law): Heat produced H = I²Rt. Applications: electric heater, electric iron, toaster, electric bulb, fuse. A fuse is a safety device with a thin wire of high resistance and low melting point — melts and breaks circuit if current exceeds safe limit. MCB (Miniature Circuit Breaker) is a modern replacement for fuse.

Common circuit components and their symbols: Cell (single), Battery (multiple cells), Bulb/lamp, Ammeter (A), Voltmeter (V), Resistor, Variable resistor (rheostat), Switch (open/closed), Wire junction, Earth connection. In a circuit diagram, components are connected using lines representing wires. Kirchhoff's laws: Junction rule — sum of currents entering = sum of currents leaving a junction. Loop rule — algebraic sum of potential differences in a closed loop = 0. Electric eel: generates electric discharge of up to 600V as a defence and hunting mechanism — example of biological electricity.

Electric current I = Q/t; SI unit ampere (1 A = 1 C/s). Conventional current flows from the positive to the negative terminal; electrons move in the opposite direction. Potential difference between two points is the work done to move a unit charge between them: V = W/Q; SI unit volt (1 V = 1 J/C). An ammeter measures current and is connected in series (low resistance). A voltmeter measures potential difference and is connected in parallel across the component (high resistance). One coulomb equals about 6.25 × 10¹⁸ electrons.

Resistance of a conductor R = ρl/A, where l is length, A is cross-sectional area and ρ is resistivity. Resistance is directly proportional to length and inversely proportional to area, so a thin long wire has more resistance. Resistivity depends on the material and temperature but not on dimensions; SI unit Ω m. Metals have low resistivity (silver 1.60 × 10⁻⁸ Ω m, copper 1.62 × 10⁻⁸ Ω m); alloys such as nichrome have higher resistivity and do not oxidise easily at high temperature, so are used in heaters. Insulators have very high resistivity. Resistance of metals rises with temperature.

When resistors are connected end to end, they are in series. The same current flows through each resistor. The total potential difference is the sum of the individual potential differences: V = V₁ + V₂ + V₃. The equivalent resistance is R = R₁ + R₂ + R₃, which is greater than the largest individual resistance. If one component breaks, the circuit is broken and the current stops. Series arrangement is not suitable for household wiring.

When resistors are connected between the same two points, they are in parallel. The potential difference across each resistor is the same. The total current is the sum of the currents in the branches: I = I₁ + I₂ + I₃. The equivalent resistance is given by 1/R = 1/R₁ + 1/R₂ + 1/R₃, and it is less than the smallest individual resistance. If one appliance fails, the others keep working. This is why household appliances are connected in parallel: each gets the full supply voltage and can be switched on and off independently.

When current flows through a resistor, electrical energy is converted into heat. Joule's law: H = I²Rt, where H is heat in joules, I is current, R is resistance and t is time. Also H = VIt = V²t/R. Applications: electric heater, iron, toaster, geyser (nichrome elements), electric bulb (tungsten filament, melting point 3380°C, glows without melting; filled with inert gas), and fuse (a wire of low-melting alloy of lead and tin, which melts and breaks the circuit when current is too high).

Power is the rate of consumption of electrical energy: P = VI = I²R = V²/R. SI unit: watt (1 W = 1 V × 1 A). Electrical energy E = P × t. The commercial unit is the kilowatt-hour (kWh): 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J, also called one 'unit' of electricity. Energy in kWh = power in kW × time in hours. Example: a 100 W bulb used for 10 h consumes 1 kWh.

Ohm's law: at constant temperature, the potential difference V across a conductor is directly proportional to the current I through it: V = IR, where R is resistance in ohms (1 Ω = 1 V/A). The V–I graph of an ohmic conductor is a straight line through the origin; its slope gives the resistance. Components that do not follow Ohm's law, like diodes and filament lamps at high temperatures, give curved V–I graphs. Resistance of a conductor rises with temperature.

Series: 4 Ω, 6 Ω and 12 Ω give R = 4 + 6 + 12 = 22 Ω. Parallel: 1/R = 1/4 + 1/6 + 1/12 = 6/12, so R = 2 Ω. Combination: 12 Ω and 6 Ω in parallel give 12 × 6 / 18 = 4 Ω; in series with 4 Ω gives 8 Ω; across 12 V the current is 1.5 A. Wire: if length doubles and area halves, the resistance becomes four times. Steps: find the equivalent resistance first, then use I = V/R, then find the branch values.

Resistance of a 100 W, 220 V bulb: R = V²/P = 220²/100 = 484 Ω. Energy used by a 1 kW iron for 2 h a day over 30 days = 60 kWh; at ₹5 per unit the cost is ₹300. Heat produced by 2 A through 10 Ω for 5 minutes: H = I²Rt = 4 × 10 × 300 = 12,000 J. Bulb at 220 V with 0.5 A: P = 220 × 0.5 = 110 W; for 2 h energy is 0.22 kWh. Always convert minutes to seconds and watts to kilowatts as required.

I = Q/t; V = W/Q; V = IR; R = ρl/A. Series: R = R₁ + R₂ + ...; parallel: 1/R = 1/R₁ + 1/R₂ + ... H = I²Rt; P = VI = I²R = V²/R; 1 kWh = 3.6 × 10⁶ J. Ammeter in series, voltmeter in parallel. Fuse is placed in series in the live wire. Alloys have higher resistivity than pure metals, so heating elements are made of nichrome and bulb filaments from tungsten.