What happens to the voltage across capacitor 1 and the stored charge when a series capacitor is added?

When a series capacitor is added to an existing capacitor in a circuit, both the voltage across the first capacitor and the stored charge experience changes due to the nature of the series configuration.

In a series connection of capacitors, the total capacitance of the circuit decreases because the formula for total capacitance (C_total) in series is given by:

1 / C_total = 1 / C1 + 1 / C2 + ...

Where C1 is the capacitance of the first capacitor and C2 is the capacitance of the added capacitor. Since the reciprocal of the capacitance is taken, the overall capacitance will be less than that of any individual capacitor in the series.

As the total capacitance decreases, for a fixed voltage applied across the series combination, the charge stored on each capacitor is given by the equation Q = C × V. With reduced capacitance, for any given applied voltage, the charge Q across capacitor 1 will also decrease because it shares the same voltage drop across the series combination. Moreover, since the voltage across the combination of capacitors is related to the charge stored on them, a decrease in the charge stored leads to decreased voltage across each capacitor, including capacitor 1.

Thus, the addition of a