Current and resistance

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
  • $\mathrm{\Delta V}=E𝓁$
  • $J=\frac{\sigma \mathrm{\Delta V}}{𝓁}$
• $R\equiv \frac{\mathrm{\Delta V}}{I}$
• $\rho =\frac{1}{\sigma }$
• $R=\rho \frac{𝓁}{A}$
• $\rho ={\rho }_0\left[1+\alpha \left(T-T_0\right)\right]$
• $\alpha =\frac{\mathrm{\Delta \rho }}{{\rho }_0\mathrm{\Delta T}}$
• $R=R_0\left[1+\alpha \left(T-T_0\right)\right]$
• $\wp =I\mathrm{\Delta V}=I^{2}R=\frac{{\mathrm{\Delta V}}^2}{R}$