What is the effect of introducing capacitors in series on total circuit capacitance?

• A. It decreases total capacitance
• B. It increases total capacitance
• C. It keeps total capacitance constant
• D. It doubles total capacitance

Answer: (A)

When capacitors are connected in series, the total capacitance of the circuit is indeed decreased compared to the individual capacitances of the capacitors. This is a fundamental principle of circuit design. The formula for the total capacitance (C_{total}) of capacitors in series is given by:

[

\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots + \frac{1}{C_n}

]

Where (C_1, C_2, \ldots, C_n) are the capacitances of the individual capacitors.

Because the reciprocal of the individual capacitances is summed, the total capacitance ends up being less than the capacitance of the smallest capacitor in the series. This reduction occurs because, in a series configuration, the charge across each capacitor must be the same and the voltage divides among them. As a result, the overall ability of the circuit to store charge (i.e., capacitance) is reduced.

In contrast, when capacitors are connected in parallel, the total capacitance would actually increase, as the total capacitance in parallel is simply the sum of the individual capacitances