**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

C=QV

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

**Capacitors in series:**

- Fig.a shows capacitors
*C*_{1}and*C*_{2}combined in series.

*Fig.a. Combination of two capacitors in series*

- The left plate of
*C*_{1}and the right plate of*C*_{2}are connected to two terminals of a battery and have charges*Q*and –*Q*, respectively. - It then follows that the right plate of
*C*_{1}has charge –*Q*and the left plate of*C*_{2}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
*C*_{1}and*C*_{2}is zero and there is no electric field in the conductor connecting*C*_{1}and*C*_{2}. - 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*_{1}and*V*_{2}across*C*_{1}and*C*_{2}, 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 (±
*Q*1) on capacitor1 and the plate charges (±*Q*2) 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