What effect does adding a third capacitor in series to a circuit with two existing capacitors have on the total capacitance and charge drawn from the battery?

When capacitors are connected in series, the total capacitance of the circuit decreases. The total capacitance ( C_{\text{total}} ) for capacitors in series can be calculated using the formula:

[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} ]

As more capacitors are added in series, the reciprocal of the total capacitance gets larger, which means that the overall capacitance decreases. This is because the system behaves similarly to a single capacitor whose capacitance is less than any of the individual capacitors connected in series.

When the capacitance decreases, the ability of the circuit to store charge also decreases. The charge ( Q ) stored in the capacitors can be calculated using the relationship:

[ Q = C_{\text{total}} \cdot V ]

where ( V ) is the voltage across the series circuit. Since the capacitance decreases when a third capacitor is added, the total charge stored in the capacitors will likewise decrease when the circuit is connected to a constant voltage source, such as a battery.

Therefore, adding