Capacitors in Series and Parallel

Systems including capacitors more than one have equivalent capacitance. Capacitors can be connected to each other in two ways. They can be connected in series and in parallel. We will see capacitors in parallel first.

In this circuit capacitors are connected in parallel.

Because, left-hand sides of the capacitors are connected to the potential a, and right-hand sides of the capacitors are connected to the potential b. In other words, we can say that each capacitor has the same potential difference. We find the charge of each capacitor as;

Q1=C1.V

Q2=C2.V

Q3=C3.V

Total charge of the system is found by adding up each charge.

Qtotal=Ceq.V

Qtotal= Q1+Q2+Q3=C1.V+C2.V+C3.V=V.(C1+C2+C3)=Ceq

Ceq=C1+C2+C3

As you can see, we found the equivalent capacitance of the system as C1+C2+C3

Now we will see the capacitors in series;

In capacitors in series, each capacitor has same charge flow from the battery. In this circuit, +Q charge flows from the positive part of the battery to the left plate of the first capacitor and it attracts –Q charge on the right plate, with the same idea, -Q charge flows from the battery to the right plate of the third capacitor and it attracts +Q on the left plate. Other capacitors are also charged with the same way. To sum up, we can say that each capacitor has the same charge with battery.

C1.V1=Q

C2.V2=Q V=V1+V2+V3 and Q=Ceq.V

C3.V3=Q

Example: Calculate the equivalent capacitance between the points a and b.

Example: In the circuit given below, C1=60µF, C2=20 µF, C3=9 µF and C4=12 µF. If the potential difference between points a an b Vab= 120V find the charge of the second capacitor.