When capacitors are connected in series, their effective capacitance (total capacitance) is different from the way it changes when they are connected in parallel. In series, the total capacitance (C_total) is inversely proportional to the sum of the inverses of the individual capacitances (C1, C2, C3, ...):
1 / C_total = 1 / C1 + 1 / C2 + 1 / C3 + ...
In other words, you calculate the reciprocal of each capacitor's capacitance, sum these reciprocals, and then take the reciprocal of the sum to find the total capacitance.
This relationship indicates that the effective capacitance decreases as you add more capacitors in series. This is because in a series configuration, the total charge stored is the same across all capacitors, and the voltage across each capacitor adds up.
It's important to note that when capacitors are connected in series, they share the same charge, but the voltage across each capacitor can be different. The voltage across each capacitor is proportional to its capacitance.
Here's a simple example: Let's say you have two capacitors, C1 and C2, connected in series with a voltage source V. The total charge Q stored on the system is the same for both capacitors:
Q = C1 * V1 = C2 * V2
The total voltage V provided by the source is the sum of the individual voltages across the capacitors:
V = V1 + V2
Since the total charge is the same for both capacitors, you can substitute Q from the first equation into the second equation:
C1 * V1 = C2 * V2
V = V1 + V2
Now, you can express V1 and V2 in terms of the total voltage V and the capacitances:
V1 = V * (C2 / (C1 + C2))
V2 = V * (C1 / (C1 + C2))
As you can see, the voltage across each capacitor is proportional to its capacitance.
When analyzing circuits with capacitors in series, it's important to consider these relationships and how they affect the overall behavior of the circuit.