PHYS 2212 Module 4.2

Capacitors in Series and in Parallel

Learning Objectives

By the end of this section, you will be able to:

• Explain how to determine the equivalent capacitance of capacitors in series and in parallel combinations
• Compute the potential difference across the plates and the charge on the plates for a capacitor in a network and determine the net capacitance of a network of capacitors

Capacitors in Series and Parallel

So far we have discussed what happens when you connect one parallel-plate capacitor to a battery. But what might happen if you connect more than one capacitor to a battery? In this section, we will look at two different ways you might connect capacitors to a battery, called Parallel and Series. 

Before we jump into that, however, let me first show you what we use to represent a battery and a capacitor in a diagram. The symbol for a battery is two parallel lines with one longer than the other:

The longer line represents the positive terminal of the battery, the side that has a higher electric potential. The shorter line in the negative terminal, which is at a lower electric potential. We usually say the negative terminal is at ground, which means V = 0 at the negative terminal. When a battery is connected to a capacitor, the positive terminal of the battery will attract electrons from the capacitor plate that directly is connected to it with a wire and the battery will use its chemical energy to push (or drive) those electrons onto the other plate of the capacitor that is directly connected to the negative terminal of the battery.

The symbol for a capacitor is two parallel lines of equal length, to represent a parallel-plate capacitor:

When a capacitor is connected to a battery with wires, the diagram would look like this:

On this diagram, since the top plate of the capacitor is connected to the positive terminal (longer line) of the battery, electrons will be pulled off of that top plate, pushed through the battery and then pushed onto the bottom plate of the capacitor. This means the top plate will have +Q on it and the bottom plate will have –Q. The amount of Q will depend on the capacitance of the capacitor and the voltage of the battery. The battery will keep moving electrons from the top plate to the bottom plate until ΔV_C = ΔV_batt. 

For capacitors connected in parallel:

For capacitors connected in series: