## Current and Resistance

• ### Units and Variables

• I - current, in amperes
• Q - charge, in coulombs
• t - time, in seconds
• J - current density, in amperes per meters squared
• E - electric field, in newtons per coulomb
• σ - conductivity
• V - electric potential, in volts
• ΔV - potential difference, in volts
• R - resistance, in ohms
• ρ - resistivity
• A - area, in meters squared
• 𝓁 - length, in meters
• α - temperature coefficient of resistivity, in ℃-1
• ℘ - electrical power, in watts
• T - temperature, in degrees celsius
• $I\equiv \frac{\mathrm{dQ}}{\mathrm{dt}}$
• $J\equiv \frac{I}{A}=\sigma E$
• For a wire
• $\mathrm{\Delta V}=E𝓁$
• $J=\frac{\sigma \mathrm{\Delta V}}{𝓁}$
• $R\equiv \frac{\mathrm{\Delta V}}{I}$
• $\rho =\frac{1}{\sigma }$
• $R=\rho \frac{𝓁}{A}$
• $\rho ={\rho }_{0}\left[1+\alpha \left(T-{T}_{0}\right)\right]$
• $\alpha =\frac{\mathrm{\Delta \rho }}{{\rho }_{0}\mathrm{\Delta T}}$
• $R={R}_{0}\left[1+\alpha \left(T-{T}_{0}\right)\right]$
• $\wp =I\mathrm{\Delta V}={I}^{2}R=\frac{{\mathrm{\Delta V}}^{2}}{R}$