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Resistance $R = \rho L/A$ depends on the material (through resistivity $\rho$) and geometry (length $L$, cross-section $A$). Resistivity $\rho = m/(ne^2\tau)$ is a material property depending on temperature, not dimensions. For metals, $\rho$ increases linearly with temperature: $\rho = \rho_0(1 + \alpha\Delta T)$, with $\alpha \sim 4 \times 10^{-3}$/K. For semiconductors, $\rho$ decreases with temperature (more carriers excited).

Key transformations: stretching a wire to $n$ times its length multiplies resistance by $n^2$ (volume conserved, so $A$ decreases by factor $n$). For combinations: series $R_{\text{eq}} = R_1 + R_2 + ...$ (current same, voltages add); parallel $1/R_{\text{eq}} = 1/R_1 + 1/R_2 + ...$(voltage same, currents add). Two in parallel:$R_{\text{eq}} = R_1R_2/(R_1+R_2)$.

The microscopic form of Ohm's law is $\vec{J} = \sigma\vec{E}$ where $\sigma = 1/\rho$ is conductivity and $\vec{J} = ne\vec{v}_d$ is current density. This connects the macroscopic observation ($V = IR$) to electron dynamics. Ohm's law is not a universal law — it fails for diodes, electrolytes, and other non-ohmic devices where $V$-$I$ is nonlinear.$