Resistance

Physics

Resistance is a measure of how much a material opposes the flow of electric current, measured in ohms; higher resistance means less current.

Visualization

Definition

Resistance is how much a material fights against electric current: thin wires, long wires, and materials like rubber have high resistance while thick copper wires have low resistance, and resistance turns electrical energy into heat, which is why toasters, hair dryers, and electric stoves are just carefully designed resistance. It is the opposition a material offers to current flow, measured in ohms, and by Ohm's law $R = V/I$; resistance increases with a conductor's length and decreases with its thickness, depends on the material, and for most metals rises with temperature. Resistance is $R = \rho L/A$, where resistivity $\rho$ is an intrinsic material property ranging from about $10^{-8}\ \Omega\cdot\text{m}$ for metals to $10^{16}$ for good insulators, and in metals $\rho(T) \approx \rho_0[1 + \alpha(T - T_0)]$ with $\alpha \approx 0.004\ \text{K}^{-1}$ for copper, because lattice vibrations scatter conduction electrons more at higher temperature; series resistances add, $R_s = \sum R_i$, parallel resistances combine as $1/R_p = \sum 1/R_i$, and superconductors have $\rho = 0$ below a critical temperature.

Example

The thin wire inside an old-style light bulb has high resistance, and current squeezing through it heats it enough to glow; a heater drawing $10\ \text{A}$ from a $120\ \text{V}$ outlet has $R = 120/10 = 12\ \Omega$ and converts $P = IV = 1{,}200\ \text{W}$ into heat, while a phone charger cable with $0.1\ \Omega$ carrying $2\ \text{A}$ wastes only $I^2R = 0.4\ \text{W}$. A $100\ \text{W}$ incandescent bulb measures $9.6\ \Omega$ cold at $20^\circ\text{C}$ but $144\ \Omega$ ($120^2/100$) when lit, and using tungsten's $\alpha = 0.0045\ \text{K}^{-1}$ gives a filament temperature near $3{,}100^\circ\text{C}$, with switch-on current $15$ times the running current, which is why bulbs usually fail the instant they turn on.

Key Insight

Adding resistors in series is like adding lengths of narrow pipe, total resistance grows, while adding them in parallel opens extra paths, so total resistance shrinks below the smallest one. Resistance is not a defect of conductors; it is the mechanism by which electrical energy becomes useful heat and light and what keeps a short circuit from being an explosion, and in a superconductor, zero resistance means a current can circulate for years without any voltage at all.