Resistance and Resistivity
Resistance depends on material properties and geometry: R = ?L/A, where R is resistance (?), ? (rho) is resistivity (??m), L is length, and A is cross-sectional area. Resistivity is a material property: copper has ? = 1.68x10?? ??m, while rubber has ? ~= 10?^3 ??m. Longer wires have more resistance; thicker wires have less. Doubling length doubles resistance; doubling area (diameter increases by sqrt2) halves resistance. This formula explains why power transmission uses thick cables and short paths when possible.
Conductors, Semiconductors, and Insulators
Materials are classified by resistivity. Conductors (metals) have low resistivity (10?? to 10?? ??m). Semiconductors (silicon, germanium) have intermediate resistivity (10?^3 to 10^3 ??m), controllable by doping. Insulators (rubber, glass, plastic) have very high resistivity (10? to 10?? ??m). Superconductors have zero resistance below critical temperature. Temperature affects resistivity-most metals increase resistance when heated (positive temperature coefficient), while semiconductors decrease (negative coefficient). Understanding these properties guides material selection for electrical applications.
Applications in Electrical Engineering
Resistance calculations are essential in circuit design. Electrical engineers select wire gauge to minimize power loss in transmission (P = I^2R). Thicker wires (lower R) reduce heating and voltage drop. Heating elements use high-resistance wire (nichrome) to convert electrical energy to heat efficiently. Fuses and circuit breakers use resistance properties to protect circuits. Resistivity measurement tests material purity and quality. Understanding resistance helps design circuits, select components, troubleshoot electrical problems, and ensure safe, efficient power distribution.
Quick Tips
- Always verify units are consistent
- Use scientific notation for very large/small numbers
- Results are approximations — real conditions may vary
Frequently Asked Questions
Resistance (?) is a property of a specific object, depending on material, length, and area. Resistivity (??m) is a material property, independent of size. Think: resistivity is like density, resistance is like mass.
Electrons must travel farther through the material, encountering more collisions with atoms. Resistance is proportional to length: R = ?L/A. Doubling length doubles resistance.
More cross-sectional area provides more paths for current, reducing resistance. R is inversely proportional to area. Doubling area (quadrupling diameter) halves resistance.
For metals, resistance increases with temperature as atomic vibrations impede electron flow. For semiconductors, resistance decreases as more charge carriers are freed. Superconductors have zero resistance below critical temperature.
Conductance (G) is the reciprocal of resistance: G = 1/R, measured in siemens (S) or mhos (?). While resistance opposes current flow, conductance measures how easily current flows. Higher conductance means easier current flow.