Themes > Science > Physics > Electromagnetism > Electrostatics > Capacitors & Dielectrics > Capacitors and Dielectrics > Capacitors in Combination > Capacitors in Combination

The symbol of a capacitor is shown in Figure 2. Capacitors can be connected together; they can be connected in series or in parallel. Figure 3 shows two capacitors, with capacitance C1 and C2, connected in parallel. The potential difference across both capacitors must be equal and therefore

 

(12)

 

 

Figure 2. Symbol of a Capacitor.

 

Figure 3. Two capacitors connected in parallel.

Using eq.(12) the total charge on both capacitors can be calculated

 

(13)

 

Equation (13) shows that the total charge on the capacitor system shown in Figure 3 is proportional to the potential difference across the system. The two capacitors in Figure 3 can be treated as one capacitor with a capacitance C where C is related to C1 and C2 in the following manner

 

(14)

 

Figure 4 shows two capacitors, with capacitance C1 and C2, connected in series. Suppose the potential difference across C1 is [Delta]V1 and the potential difference across C2 is [Delta]V2. A charge Q on the top plate will induce a charge -Q on the bottom plate of C1. Since electric charge is conserved, the charge on the top plate of C2 must be equal to Q. Thus the charge on the bottom plate of C2 is equal to -Q. The voltage difference across C1 is given by

 

(15)

 

and the voltage difference across C2 is equal to

 

(16)

 

 

Figure 4. Two capacitors connected in series.

The total voltage difference across the two capacitors is given by

 

(17)

Equation (17) again shows that the voltage across the two capacitors, connected in series, is proportional to the charge Q. The system acts like a single capacitor C whose capacitance can be obtained from the following formula

 

(18)


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