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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.
The capacitors carry the following charges: 
The total charge Q that is generated by a direct current source is equal to the sum of the individual charges:
Summing the values in parentheses gives the total capacitance C for a parallel circuit:
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.
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:
The total potential is equal to the sum of the individual potentials:
Consequently, the total capacitance of a series-connection is given by the following:
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?
