You make a capacitor by cutting the 15.0-cm -diameter bottoms out of two aluminum pie plates, se

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You make a capacitor by cutting the 15.0-cm -diameter...

You make a capacitor by cutting the $15.0-\mathrm{cm}$ -diameter bottoms out of two aluminum pie plates, separating them by 3.50 $\mathrm{mm},$ and connecting them across a $6.00-\mathrm{V}$ battery. (a) What's the capacitance of your capacitor? (b) If you disconnect the battery and separate the plates to a distance of $3.50 \mathrm{~cm}$ without discharging them, what will be the potential difference between them?

Key Concepts

Parallel Plate Capacitor

A parallel plate capacitor is a fundamental configuration that consists of two conductive plates separated by a small distance. The capacitance of such a capacitor is determined by the area of the plates and the distance between them, expressed by the formula C = ??(A/d) for a vacuum (or adjusted for a dielectric medium). This concept is central to understanding how physical dimensions and material properties influence a capacitor’s ability to store electrical energy.

Capacitance

Capacitance is a measure of a capacitor's ability to store electric charge per unit potential difference across its plates. It is defined by the equation C = Q/V, where Q is the charge and V is the voltage. The capacitance is influenced by the geometry of the capacitor and the dielectric properties of the material between the plates, making it a critical parameter in the design and function of electronic circuits.

Charge Conservation in Capacitors

Charge conservation is a fundamental principle stating that the total electric charge in an isolated system remains constant. When a capacitor, disconnected from a voltage source, undergoes a change such as an increase in plate separation, its stored charge remains unchanged. This principle, in conjunction with the capacitance formula, is used to determine how changes in the capacitor’s geometry affect the voltage across the plates.