Three capacitors having capacitances of 8.4,8.4, and 4.2μF are connected in series across a 36-V

Three capacitors having capacitances of 8.4,8.4, and 4.2μF...

Three capacitors having capacitances of $8.4,8.4,$ and 4.2$\mu \mathrm{F}$ are connected in series across a $36-\mathrm{V}$ potential difference. (a) What is the charge on the $4.2-\mu F$ capacitor? (b) What is the total energy stored in all three capacitors? (c) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination? (d) What is the total energy now stored in the capacitors?

Key Concepts

Series Connection of Capacitors

When capacitors are connected in series, the same charge accumulates on each capacitor regardless of their individual capacitances. This is due to the fact that the current that flows through every capacitor in series is the same, leading to equal quantities of charge being stored on each. Calculations involving series capacitors often require determining the equivalent capacitance, which is less than any individual capacitor's value in the series.

Equivalent Capacitance

The equivalent capacitance of capacitors connected in series is found using the reciprocal formula: 1/C_eq = 1/C1 + 1/C2 + ... . This value represents the overall capacitance of the series network and is useful for simplifying complex circuits. Once determined, it is used to calculate quantities like the total charge stored when the system is subjected to an external potential difference.

Energy Storage in Capacitors

A capacitor stores energy in an electric field, and the energy stored can be calculated using formulas such as U = ½CV² or U = ½QV, where C represents the capacitance, V the voltage, and Q the charge on the capacitor. Understanding energy storage is important when analyzing changes in the circuit configuration, as reconfigurations can lead to energy redistribution and sometimes energy losses.

Charge Redistribution and Reconfiguration to Parallel Connection

When capacitors that were charged in series are reconnected in parallel, with like plates connected together, the stored charges redistribute among the capacitors. In this configuration, the voltage across each capacitor becomes the same, and the final voltage can be determined using conservation of charge. Notably, while charge is conserved, energy is not necessarily conserved due to possible dissipation during the redistribution process.