Electricity Essentials

Cheatsheet Content

Electric Current and Circuit Electric Current: Rate of flow of electric charges. Formula: $I = \frac{Q}{t}$ $I$: Current (Amperes, A) $Q$: Charge (Coulombs, C) $t$: Time (seconds, s) SI Unit of Charge: Coulomb (C) Charge of 1 electron: $1.6 \times 10^{-19}$ C 1 Ampere: $1 \text{ A} = 1 \text{ C/s}$ Smaller Units: $1 \text{ mA} = 10^{-3} \text{ A}$ $1 \mu\text{A} = 10^{-6} \text{ A}$ Ammeter: Instrument to measure electric current, always connected in series. Conventional Current Direction: From positive to negative terminal, opposite to electron flow. Electric Circuit: A continuous and closed path of an electric current. Electric Potential and Potential Difference Potential Difference (V): Work done to move a unit charge from one point to another. Formula: $V = \frac{W}{Q}$ $V$: Potential difference (Volts, V) $W$: Work done (Joules, J) $Q$: Charge (Coulombs, C) SI Unit: Volt (V) 1 Volt: $1 \text{ V} = 1 \text{ J/C}^{-1}$ Voltmeter: Instrument to measure potential difference, always connected in parallel. Circuit Diagram Symbols Component Symbol Electric Cell Battery Plug Key (open) Plug Key (closed) Wire Joint Wires crossing without joining Electric Bulb Resistor (R) Variable Resistor/Rheostat Ammeter A Voltmeter V Ohm's Law Statement: The potential difference ($V$) across a conductor is directly proportional to the current ($I$) flowing through it, provided its temperature remains constant. Formula: $V = IR$ $V$: Potential difference (Volts, V) $I$: Current (Amperes, A) $R$: Resistance (Ohms, $\Omega$) Resistance: Property of a conductor to resist the flow of charges. SI Unit of Resistance: Ohm ($\Omega$). 1 Ohm: $1 \Omega = \frac{1 \text{ V}}{1 \text{ A}}$ Rheostat: A device used to change the resistance in a circuit without changing the voltage source. Factors Affecting Resistance Resistance of a uniform metallic conductor is: Directly proportional to its length ($l$): $R \propto l$ Inversely proportional to its area of cross-section ($A$): $R \propto \frac{1}{A}$ Depends on the nature of its material. Formula: $R = \rho \frac{l}{A}$ $\rho$: Electrical resistivity of the material $l$: Length of the conductor $A$: Area of cross-section SI Unit of Resistivity: Ohm-meter ($\Omega \text{ m}$) Conductors: Low resistivity (e.g., metals like Silver, Copper). Insulators: High resistivity (e.g., rubber, glass). Alloys: Generally higher resistivity than constituent metals, do not oxidize easily, used in heating devices. Resistors in Series Connection: Resistors are joined end-to-end. Current: Same current flows through each resistor. Potential Difference: Total potential difference is the sum of individual potential differences: $V = V_1 + V_2 + V_3 + ...$ Equivalent Resistance ($R_s$): Sum of individual resistances: $R_s = R_1 + R_2 + R_3 + ...$ Disadvantages: Current is constant, impractical for devices needing different currents. If one component fails, the entire circuit breaks. Resistors in Parallel Connection: Resistors are connected between two common points. Potential Difference: Same potential difference across each resistor. Current: Total current is the sum of currents through individual branches: $I = I_1 + I_2 + I_3 + ...$ Equivalent Resistance ($R_p$): Reciprocal of equivalent resistance is the sum of reciprocals of individual resistances: $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$ Advantages: Current divides, allowing devices needing different currents to operate. If one component fails, others continue to work. Total resistance is decreased. Heating Effect of Electric Current (Joule's Law of Heating) Concept: When current flows through a resistor, electrical energy is converted into heat. Heat Generated (H): $H = VIt$ Using Ohm's Law ($V=IR$): $H = I^2Rt$ Using Ohm's Law ($I=V/R$): $H = \frac{V^2}{R}t$ Factors: Heat produced is directly proportional to: Square of current ($I^2$) Resistance ($R$) Time ($t$) for which current flows Applications: Electric heating devices (iron, toaster, kettle). Electric bulbs (filament heats up and emits light, typically tungsten with high melting point, filled with inactive gases like nitrogen/argon). Electric fuse: Protects circuits by melting and breaking the circuit if current exceeds safe limit. Made of metal/alloy with appropriate melting point. Electric Power Definition: Rate at which electric energy is dissipated or consumed. Formulas: $P = VI$ Using Ohm's Law: $P = I^2R$ Using Ohm's Law: $P = \frac{V^2}{R}$ SI Unit: Watt (W) 1 Watt: $1 \text{ W} = 1 \text{ V} \times 1 \text{ A}$ Commercial Unit of Electrical Energy: Kilowatt-hour (kWh) Conversion: $1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$