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Capacitors In Series

When the negative plate of one capacitor is connected to the positive plate of another capacitors, as shown in the capacitors are said to be connected in series.

If several capacitors connected in series are put across a potential difference of V volts. as shown, then the electrons will flow from plate A to plate B and so on up to plate G from will where they will pass to the positive terminal of the source of supply. Thus all the capacitors will get the same charge, let it be Q coulombs.

Let the potential differences across the capacitors of capacitances C1, C2 and C3 be V1, V2 and V3 respectively.

Now potential difference across the capacitor of capacitance  C1, V1 = Q

Similarly p.d across capacitor of capacitance  C2, V2 = Q

and P.D. across the capacitor of capacitance  C3, V3 = Q

P.D. applied across the system, V = V1+ V2 + V3

or                      V = Q + Q + Q
                              C1   C2  C3

or                      V = = 1 1
                         Q   C1   C2  C3

If C is the equivalent capacitance of the system then by definition

              C = Charge on the system   = Q
                    P.D. across the system    V

or                  1 = 1  + 1 + 1  
                    C    C1   C2  C3

Thus when numbers of capacitors are connected in series the reciprocal of the equivalent capacitance of the system is given by the arithmetic sum of the reciprocals of their individual capacitances.

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