Monday, December 31, 2012

Grouping of Capacitors

Capacitors in series

Figure shows capacitors C1 and C2 combined in series.

The left plate of C1 and the right plate of C2 are connected to two terminals of a battery and have charges Q and –Q, respectively.

It then follows that the right plate of C1 has charge –Q and the left plate of C2 has charge Q. If this was not so, the net charge on each capacitor would not be zero.

This would result in an electric field in the conductor connecting C1and C2. Charge would flow until the net charge on both C1 and C2 is zero and there is no electric field in the conductor connecting C1 and C2. Thus, in the series combination, charges on the two plates (±Q) are the same on each capacitor.

The total potential drop V across the combination is the sum of the potential drops V and V across C and C, respectively.

Following the same steps as for the case of two capacitors, we get the general formula for effective capacitance of a series combination of n capacitors:

Capacitors in parallel

Figure shows two capacitors arranged in parallel. In this case, the same potential difference is applied across both the capacitors.

But the plate charges (±Q1) on capacitor 1 and the plate charges (±Q2) on the capacitor 2 are not necessarily the same:

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