. C OMBINATION OF C APACITORS We can combine several capacitors of capacitance C , C ,…, C n to obtain a system with some effective capacitance C . The effective capacitance depends on the way the individual capacitors are combined. Two simple possibilities are discussed below.
. . Capacitors in series Figure . shows capacitors C and C combined in series.
The left plate of C and the right plate of C are connected to two terminals of a battery and have charges Q and – Q , respectively. It then follows that the right plate of C has charge – Q and the left plate of C 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 C and C .
Charge would flow until the net charge on both C and C is zero and there is no electric field in the conductor connecting C and C . 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. V = V + V = Q Q ( .
) i.e., Q , ( . ) Now we can regard the combination as an effective capacitor with charge Q and potential difference V . The effective capacitance of the combination is Q ( . ) We compare Eq.
( . ) with Eq. ( . ), and obtain ( .
) FIGURE . Combination of two capacitors in series. FIGURE . Combination of n capacitors in series.