The 300 μF capacitor in FIGURE P30.75 is initially charged to 100 V, the 1200 μF capacitor is uncharged, and the switches are both open.<IMAGE>
a. What is the maximum voltage to which you can charge the 1200 μF capacitor by the proper closing and opening of the two switches?

Key Concepts

Capacitance

Capacitance is the ability of a capacitor to store electrical charge per unit voltage. It is measured in farads (F) and is defined as the ratio of the charge (Q) stored on one plate of the capacitor to the voltage (V) across the plates, expressed as C = Q/V. In this problem, understanding the capacitance values of the capacitors involved is crucial for calculating the charge and voltage changes when the switches are manipulated.

Voltage Division

Voltage division is a principle used in circuits to determine the voltage across components in series. When capacitors are connected in series, the total voltage across the series is divided among the capacitors based on their capacitance values. This concept is essential for predicting how the voltage will distribute between the 300 μF and 1200 μF capacitors when the switches are closed, allowing for the calculation of the maximum voltage on the 1200 μF capacitor.

Energy Conservation in Capacitors

The principle of energy conservation states that energy cannot be created or destroyed, only transformed. In the context of capacitors, the energy stored in a capacitor is given by the formula U = 1/2 CV². When transferring charge between capacitors, the total energy before and after the transfer must remain constant, which is key to determining the maximum voltage that can be achieved on the 1200 μF capacitor after the switches are manipulated.