Ohm's law for current i flowing in a circuit with resistance R and potential V is

 

iR = V

 

Capacitance is defined as

 

V = q / C,

 

where V is the potential across the capacitance, and q is the charge.

 

Consider a circuit containing a resistance and a capacitance. Let us examine the above equations, using dimensional analysis. We will use brackets to indicate the dimensions.

 

[iR] = [q / C], or

 

[RC] = [q / i] = [t].

 

The produce RC has dimensions of time. What kind of time could there be?

 

If we have a battery and close the switch, current will flow, and the capacitor will become charged. However, this will not take place instantaneously, as nothing in physics takes place instantaneously. The time constant is RC. This means after this time, most of the action will have taken place. It turns out that using calculus we can get the function, which is exponential. The point here is that without knowing the exact function, we have some idea, just using dimensional analysis.