Electricity - Class 10 Science

Cheatsheet Content

Electric Current and Circuit Electric Current ($I$): Rate of flow of electric charge. $I = \frac{Q}{t}$ (where $Q$ is charge, $t$ is time) SI unit: Ampere (A). $1 \text{ A} = 1 \text{ C/s}$ Direction: Opposite to flow of electrons (conventional current). Electric Charge ($Q$): $Q = ne$ (where $n$ is number of electrons, $e$ is charge of one electron) $e = 1.6 \times 10^{-19} \text{ C}$ SI unit: Coulomb (C). Electric Circuit: A continuous and closed path of electric current. Ammeter: Measures current. Connected in series. Low resistance. Electric Potential and Potential Difference Electric Potential Difference ($V$): Work done to move a unit charge from one point to another. $V = \frac{W}{Q}$ (where $W$ is work done, $Q$ is charge) SI unit: Volt (V). $1 \text{ V} = 1 \text{ J/C}$ Voltmeter: Measures potential difference. Connected in parallel. High resistance. Galvanometer: Detects presence and direction of current. Ohm's Law States that the current ($I$) flowing through a conductor is directly proportional to the potential difference ($V$) across its ends, provided its temperature and other physical conditions remain unchanged. $V \propto I \implies V = IR$ Where $R$ is the constant of proportionality, called Resistance. Resistance ($R$): Opposition to the flow of electric current. SI unit: Ohm ($\Omega$). $1 \Omega = 1 \text{ V/A}$ Factors affecting Resistance: $R \propto L$ (Length of conductor) $R \propto \frac{1}{A}$ (Area of cross-section) $R = \rho \frac{L}{A}$ (where $\rho$ is resistivity) Resistivity ($\rho$): Resistance of a conductor of unit length and unit cross-sectional area. SI unit: Ohm-meter ($\Omega \text{m}$) Depends on material, not dimensions. Metals have low resistivity (good conductors). Insulators have high resistivity. Combination of Resistors 1. Resistors in Series Current is same through each resistor. Total voltage is sum of individual voltages: $V = V_1 + V_2 + V_3$ Equivalent Resistance ($R_S$): $R_S = R_1 + R_2 + R_3 + ...$ $R_S$ is greater than the greatest individual resistance. 2. Resistors in Parallel Voltage is same across each resistor. Total current is sum of individual currents: $I = I_1 + I_2 + I_3$ Equivalent Resistance ($R_P$): $\frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$ $R_P$ is less than the least individual resistance. Heating Effect of Electric Current (Joule's Law) When current flows through a resistor, electrical energy is converted into heat energy. $W = VQ = VIT$ Using $V=IR$, $W = I^2RT$ Using $I=V/R$, $W = \frac{V^2}{R}T$ Heat Produced ($H$): $H = I^2RT$ (in Joules) Applications: Electric heater, electric iron, electric bulb (filament heats up and glows), fuses. Electric Fuse: Safety device, usually made of an alloy of lead and tin, with low melting point. Breaks circuit if current exceeds safe limit. Electric Power Electric Power ($P$): Rate at which electrical energy is consumed or dissipated. $P = \frac{W}{t} = VI$ Using $V=IR$, $P = I^2R$ Using $I=V/R$, $P = \frac{V^2}{R}$ SI unit: Watt (W). $1 \text{ W} = 1 \text{ J/s}$ Commercial Unit of Energy: Kilowatt-hour (kWh). $1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$ $1 \text{ kWh} = 1 \text{ unit}$ of electricity. Common Symbols in Circuit Diagrams Component Symbol Electric Cell Battery Switch (Open) Switch (Closed) Wire Joint Wires Crossing (No Join) Electric Bulb Resistor Variable Resistor (Rheostat) Ammeter A Voltmeter V Galvanometer G