Two parallel-plate capacitors, 8.0 μF each, are connected in parallel to a 10 V battery. One of

Two parallel-plate capacitors, 8.0 μF each, are connected in...

Two parallel-plate capacitors, $8.0 \mu \mathrm{F}$ each, are connected in parallel to a $10 \mathrm{~V}$ battery. One of the capacitors is then squeezed so that its plate separation is $50.0 \%$ of its initial value. Because of the squeezing, (a) how much additional charge is transferred to the capacitors by the battery and (b) what is the increase in the total charge stored on the capacitors?

Key Concepts

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by an insulating material (dielectric). Its capacitance is determined by the area of the plates, the distance between them, and the dielectric constant of the material between the plates. This model is fundamental in understanding how capacitors store electrical energy in the form of an electric field.

Dependence of Capacitance on Plate Separation

The capacitance of a parallel-plate capacitor is inversely proportional to the separation between its plates. Reducing the distance increases the capacitance, as long as other factors such as the plate area and dielectric constant remain constant. This concept is crucial when analyzing physical changes to capacitors, such as squeezing one to decrease its separation.

Constant Voltage Source (Battery) and Charge Redistribution

When a capacitor is connected to a constant voltage source, like a battery, the voltage across it remains fixed. As the capacitance changes, the charge stored (given by Q = CV) adjusts accordingly. In such circuits, any increase in capacitance due to physical modification leads to a corresponding additional charge being supplied by the battery.

Parallel Connection of Capacitors

In a parallel arrangement, capacitors share the same voltage across their terminals. The total capacitance is the sum of the individual capacitances, and the total charge stored is the sum of the charges on each capacitor. This configuration is important for analyzing how modifications to one capacitor affect the overall system's stored charge.