gabriel109 said:
I had a hard time understanding that while the capacitor is charging the negative terminal and the negative plate are not at the same potential.
I'm not sure exactly what you mean, but, yes they are at the same potential (assuming the conductivity of the wires is insignificant compared to the rest of the circuit).
Let's consider your drawing with the grounding electrode connected back to the battery cathode (-) through the earth with some resistance.
- When the switch closes, the capacitor voltage is zero and stays at zero.
- This will make the grounding electrode rise to the battery anode potential (+).
- This, in turn, will cause current to flow through the circuit, limited by the resistance of the soil.
- The current flowing through the capacitor will cause it to charge up, perhaps slowly.
- The increased voltage drop across the capacitor will reduce the voltage of the grounding electrode.
- The decreasing voltage of the grounding electrode will cause reduced current flow through the earth according to Ohm's Law.
- The decreasing current flow will still charge the capacitor voltage, but at a slower rate. The result will be an exponential response of both the capacitor voltage and the current.
- Eventually, the grounding electrode will approach the same voltage as the battery cathode (-), and the capacitor voltage will approach the battery voltage.
The capacitor voltage only changes in proportion to the amount of charge that has passed through it. The rest of the circuit is significant in determining what that current flow is. Initially, all of the battery voltage is applied across the soil resistance, later it will all be across the capacitor.
In the drawing from the book, with no earth resistance, the current will be limited by other resistances, like internal to the battery, or the connecting wires. When the resistance gets very small, there are other much more complex things happening with the generated magnetic fields that limit the current (that should be a different thread, really).