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Series and Parallel Connection of Capacitors

Parallel Connection of Capacitors:

The diagram below shows an example of capacitors connected in parallel. In this case, the same voltage U is present across all capacitors. 

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

The capacitors carry the following charges: CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

The total charge Q that is generated by a direct current source is equal to the sum of the individual charges: 

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

Summing the values in parentheses gives the total capacitance C for a parallel circuit:

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

In other words:

The total capacitance of capacitors connected in parallel is equal to the sum of the individual capacitances.

Connecting capacitors in parallel is equivalent to increasing the plate area.

Series Connection of Capacitors:

Connecting several capacitors in series to a voltage source as shown in the diagram below causes a charge Q to be transported through the entire circuit. 

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

The effect of this is that each of the capacitors must have this same charge Q induced across it. The voltage Ui across each of the components is then dependent on the corresponding capacitances: 

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

The total potential is equal to the sum of the individual potentials:

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

Consequently, the total capacitance of a series-connection is given by the following:

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

In other words:

For capacitors connected in series, the inverse of the total capacitance is equal to the sum of the inverses of the individual capacitances.

In this case, the total capacitance is less than the smallest individual capacitance. Connecting capacitors in series is equivalent to increasing the plate spacing.

What is the total capacitance C of the following circuit comprising four capacitors?

CAPACITOR IN ALTERNATING CURRENT AC CIRCUITS !

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