A 10.0 -parallel-plate capacitor is connected to a 12.0 -V...

A 10.0 -\muF parallel-plate capacitor is connected to a 12.0 -V battery. After the capacitor is fully charged, the battery is disconnected without loss of any of the charge on the plates. (a) A voltmeter is connected across the two plates without discharging them. What does it read? (b) What would the voltmeter read if (i) the plate separation were doubled; (ii) the radius of each plate were doubled but their separation was unchanged?

Key Concepts

Effect of Geometric Modifications on Voltage

Alterations to the capacitor’s physical structure, such as doubling the plate separation or doubling the plate radius, impact its capacitance and thus the voltage across the plates when the charge remains constant. Doubling the separation decreases the capacitance, leading to an increase in voltage, whereas doubling the plate radius (which increases the area and hence the capacitance) results in a decrease in voltage. Understanding these effects is key to predicting how circuit behavior changes with mechanical adjustments.

Voltage-Charge-Capacitance Relationship

The relationship between the voltage (V), charge (Q), and capacitance (C) of a capacitor is given by the equation V = Q/C. This formula indicates that if the capacitance changes while the charge remains fixed (as in an isolated system), the voltage across the capacitor will change accordingly. This concept is essential when analyzing how modifications to the capacitor’s geometry affect its voltage reading.

Conservation of Charge in Isolated Systems

When a charged capacitor is disconnected from its battery, the total charge on its plates remains constant. This principle of charge conservation is crucial because any subsequent changes in the capacitor’s geometry (such as altering the plate separation or area) will affect the voltage across the plates rather than the amount of stored charge.

Capacitance and Its Dependence on Geometry

The capacitance of a capacitor is determined by its physical characteristics, namely the area of the plates, the distance between the plates, and the permittivity of the medium between them. For a parallel?plate capacitor, increasing the plate area increases the capacitance, while increasing the separation between the plates decreases the capacitance. This relationship underscores how changes in geometry affect the ability of the capacitor to store charge.

Parallel?Plate Capacitor

A parallel?plate capacitor consists of two conductive plates separated by a gap (often filled with an insulator). Its basic operation involves storing electrical energy in the electric field created between the plates when they are charged. This fundamental concept is central to understanding how energy is stored and how voltage differences arise in electric circuits.

Transcript

Please give Ace some feedback