Question

Which statement accurately describes the effect of connecting capacitors in series on the total capacitance of the circuit?

Option 1: Connecting capacitors in series decreases the total capacitance by increasing the distance between the capacitor plates.
Option 2: Connecting capacitors in series increases the total capacitance by reducing the distance between the capacitor plates.
Option 3: Connecting capacitors in series has no effect on the total capacitance of the circuit.
Option 4: The effect of connecting capacitors in series on the total capacitance depends on the specific capacitance values of the capacitors being used.

Answer 1

Connecting capacitors in series decreases the total capacitance; the equivalent capacitance is smaller than the smallest individual capacitance in the series.

Step-by-step explanation:

When connecting capacitors in series, the total capacitance of the circuit decreases. This effect is due to the fact that the charge on the series combination of capacitors is the same across all capacitors, and each capacitor experiences a voltage drop that depends on its individual capacitance. The reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances in the series. Therefore, Option 1 correctly describes the effect of connecting capacitors in series, which is that it decreases the total capacitance by effectively increasing the distance between the capacitor plates.

To illustrate, consider a series combination of a 2 F and a 3 F capacitor. The equivalent total capacitance (Ceq) can be calculated using the formula 1/Ceq = 1/C1 + 1/C2, where C1 and C2 are the capacitances of the individual capacitors. Therefore, 1/Ceq = 1/2 + 1/3 = 3/6 + 2/6 = 5/6, and Ceq = 6/5 or 1.2 F, which is less than the smallest individual capacitance in the series.