Capacitor Connection Conundrum?

📌 CONCEPT: When capacitors are connected in series and then in parallel, the charge stored in each capacitor is the same in both configurations, but the potential difference across them changes accordingly.

📐 RULE / FORMULA: The key principle is that the charge stored in each capacitor is the same when connected in series or parallel, but the potential difference is inversely proportional to the capacitance.

💡 WORKED EXAMPLE: Consider two capacitors, C1 = 40 μF and C2 = 20 μF, connected in series across a 400 V power supply. When they are disconnected and connected in parallel, the charge stored in each capacitor can be calculated as Q = CV, where C is the equivalent capacitance of the parallel combination. The equivalent capacitance is given by 1/Ceq = 1/C1 + 1/C2. Solving for Ceq, we get Ceq = (C1*C2) / (C1 + C2). Substituting the given values, Ceq = (40*20) / (40 + 20) = 16 μF. Now, the charge stored in each capacitor is Q = VCeq = 400*16 = 6400 μC. Since the capacitors are identical, each stores 3200 μC of charge in the parallel configuration.

⚠️ COMMON MISTAKE: Students often forget to calculate the equivalent capacitance of the parallel combination and directly use the individual capacitances, leading to incorrect charge storage values.