Combination of Capacitors – Parallel and Series

How Capacitors are connected?

Capacitors combination can be made in many ways. The combination is connected to a battery to apply a potential difference (V) and charge the plates (Q). We can define the equivalent capacitance of the combination between two points to be

Two frequently used methods of combination are: Parallel combination and Series combination.

Capacitors in series:

• Fig.a shows capacitors C₁ and C₂ combined in series.

Fig.a. Combination of two capacitors 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 ofC₁ 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.
• The 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 V₁ and V₂ across C₁ and C₂, respectively.

• The effective capacitance of the combination is

So,

• For n capacitor arranged in series (Fig. b)

Fig.b Combination of n capacitors in series

• The total potential drop V of a series combination of n capacitor is

• Effective capacitance of a series combination of n capacitors,

Capacitors in Parallel:

• Fig. a, shows two capacitors arranged in parallel.

Fig. Parallel combination of two capacitors

• In this case, the same potential difference is applied across both the capacitors. But the plate charges (±Q1) on capacitor1 and the plate charges (±Q2) on the capacitor 2 are not necessarily the same:

• The equivalent capacitor is one with charge

and potential difference V.

• The effective capacitance C is,

• The general formula for effective capacitance C for parallel combination of n capacitors

Fig. Parallel combination of n capacitors

• If N identical capacitors of capacitance C are connected in series, then effective capacitance = C/N
• If N identical capacitors of capacitance C are connected in parallel, then effective capacitance = CN