Capacitors in Series and Parallel with Examples

 

Capacitors in Series and Parallel

Systems including capacitors more than one has 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.

capacitors 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 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;

capacitors in series

 

 

 

 

 

 

 

 

 

In capacitors in series, each capacitor has same charge flow from 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 same way. To sum up we can say that each capacitor has same charge with batter.

C1.V1=Q

C2.V2=Q , V=V1+V2+V3 and Q=Ceq.V

C3.V3=Q

capacitors in series equation

 

 

 

 

 

 

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

 

capacitors example

 

 

 

capacitors example

 

 

 

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.

capacitors example

 

 

 

capacitors example

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Electrostatics Exams and Solutions

 

 

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