Charging a capacitor is an example of a non steady current. Think about what happens in the circuit below:
At t = 0 the switch S is closed. What happens?
Take a moment to write in your journal what you think will happen to
The way to analyze the problem is to start with Kirchoff's rules. There is only one branch to the circuit so there is only one current and one loop to sum potentials. Taking the current to flow clockwise, Positive charge will pile up on the top plate of the capacitor. Current flows downhill through the resistor which means the left side of the resistor is positive giving the polarities shown below.
Going clockwise around the loop in the same direction as the current gives a potential rise through the battery, a potential drop of - IR through the resistor, and a potential drop of - Q/C through the capacitor.
Initially there is no charge on the capacitor so the potential drop across it is zero, thus the whole potential drop supplied by the battery must appear across the resistor creating the moment of largest current.
As charge builds on capacitor it accumulates some of the potential drop from the battery. The potential drop on the resistor necessarily decreases to match the gain on the capacitor. This means the current begins to fall. Eventually the capacitor will gain all of the potential drop and that supplies by the resistor will be zero.
The process of charging a capacitor is just a wholesale shift in the charge distribution rather than a flow of charge from the battery to the capacitor. In the movie below, shifting the positive charges somewhat leaves net positive charge on the top plate and a deficit of positive charge on the bottom plate. A deficit of positive charge means the bottom plate is negatively charged.
Go to Exercise 2.