Final answer:
To determine the charge stored in capacitor Y after switch S1 is closed, one must find the equivalent series capacitance of X and Y, then calculate the total charge using the formula Q = C * V, where V is 120 V.
Step-by-step explanation:
The question is asking us to determine how much charge is stored in capacitor Y after switch S1 is closed (with S2 remaining open) and a potential difference of 120 V is applied between points a and b. To solve this, we need to understand that since capacitors X and Y are connected in series, they will each hold the same amount of charge Q. This is because in a series circuit, charge does not split between components; rather, the same charge moves through each component.
The charge Q on a capacitor can be calculated using the formula Q = C * V, where C is the capacitance and V is the potential difference across the capacitor. However, before we can use this formula, we need to find the equivalent series capacitance of capacitors X and Y, because the 120 V is actually the total potential difference across both X and Y together.
Once the equivalent capacitance Ceq is found, the total charge Q on the series combination can be calculated with the applied voltage (120 V). This same charge Q will be present on each capacitor. To find the individual capacitances and calculate Ceq for capacitors X and Y, we would need their specific values which are not provided in the question. Assuming that they are available, the equivalent capacitance for a series connection is calculated as 1/Ceq = 1/CX + 1/CY. After finding Ceq, we can then find the charge Q using the formula Q = Ceq * V. This charge Q will be the answer to how much charge is stored in capacitor Y.