Resistivity Materials Table

Electrical Resistivity (symbol $\rho$, pronounced 'rho') is a fundamental property of a material that quantifies how strongly it resists electric current. Unlike Resistance ($R$), which depends on the wire's length and thickness, Resistivity is a property of the material itself. A copper wire has different resistance depending on its size, but copper always has the same resistivity ($1.68 \times 10^{-8} \Omega \cdot m$).

Think of water flowing through a pipe. Resistivity ($ ho$) is like the roughness of the pipe's inner wall (concrete vs. plastic)—it depends only on the material. Resistance ($R$) is how hard it is to push water through the entire pipe—it depends on the roughness ($ ho$) BUT ALSO on how long ($L$) and how narrow ($A$) the pipe is. Formula: $R = \rho L / A$.

In conductors like copper, electric current is the flow of free electrons. As the metal gets hotter, the atoms in the crystal lattice vibrate more violently. These vibrating atoms collide with the flowing electrons more frequently, scattering them and dragging them down. This increased 'atomic friction' is observed as higher resistance.

Silicon is a Semiconductor. At low temperatures, its electrons are stuck in bonds and can't flow. Adding heat provides enough energy to break these bonds, freeing up more electrons (charge carriers) to conduct current. This effect (more free carriers) overpowers the increased vibration effect, so total resistance drops. This is why Silicon has a negative temperature coefficient ($\alpha$).

The Temperature Coefficient of Resistance ($\alpha$) tells you how much the resistance changes for every 1°C rise in temperature. For Copper, $\alpha \approx 0.0039$. This means for every 100°C rise, the resistance increases by about 39%. The formula is $R_{new} = R_{ref} [1 + \alpha (T_{new} - T_{ref})]$.

Silver is the best conductor with the lowest resistivity ($1.59 \times 10^{-8} \Omega \cdot m$). However, Silver is expensive and tarnishes. Copper is the second-best ($1.68 \times 10^{-8}$) and is widely used because it is much cheaper, ductile, and corrosion-resistant.

Copper corrodes (rusts) over time, forming an insulating oxide layer. Gold is chemically inert—it never corrodes. In computers and phones, vital connectors are gold-plated to ensure a perfect, reliable connection causing zero signal loss over the device's lifetime, even though Gold's conductivity is actually lower than Copper's.

It's all about Band Theory. In insulators (like glass or rubber), there is a large energy gap (Band Gap) between the valence electrons (stuck to atoms) and the conduction band (where they can flow). Electrons can't jump this gap under normal conditions, so no current flows. In conductors, these bands overlap.

Superconductivity is a quantum phenomenon where a material's resistivity drops strictly to ZERO. This usually happens at extremely low temperatures (near Absolute Zero, -273°C). In a superconductor, electrons form 'Cooper Pairs' that move through the lattice without ever colliding, meaning current can loop forever with zero energy loss.

Conductivity (symbol $\sigma$, sigma) is simply the reciprocal (inverse) of Resistivity. If Resistivity measures how much a material stops flow, Conductivity measures how well it allows flow. Formula: $\sigma = 1 / \rho$. The unit is Siemens per meter (S/m).