Current

Just as how water flow would be measured in kg/s, current is in units of C/s (aka an Amp) and represented by the symbol \(I\). \(I = \frac{\Delta V}{\text{Resistance}}\)

Therefore \(\text{Resistance} = R = \frac{J}{C} \cdot \frac{s}{C} = \frac{Js}{C^2} = \text{Ohm} = \Omega\)

Resistance increases with longer or skinnier wires, so \(R = \frac{L}{A} \cdot \text{Resistivity of material}\). Resisitivity is in units of \(\Omega m\) and denoted by \(\rho\).

Current can be thought of as \(\frac{dQ}{dt}\).
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