Give as clear an explanation as possible as to why it is...

Name: Problem 59, Chapter 28: Understanding Physics
Uploaded: 2021-09-04T01:51:23-08:00
Duration: 2 min 28 s
Channel: Vishal Gupta
Description: Give as clear an explanation as possible as to why it is physically reasonable to expect that two identical parallel-plate capacitors placed in parallel ought to have twice the capacitance as one capacitor. Hints: What happens to the effective area of capacitors wired in parallel? What does the fact that like charges repel and opposites attract have to do with anything?

Give as clear an explanation as possible as to why it is physically reasonable to expect that two identical parallel-plate capacitors placed in parallel ought to have twice the capacitance as one capacitor. Hints: What happens to the effective area of capacitors wired in parallel? What does the fact that like charges repel and opposites attract have to do with anything?

Key Concepts

Capacitance

Capacitance is a measure of a capacitor's ability to store electrical charge per unit voltage. In the context of a parallel-plate capacitor, capacitance is directly proportional to the plate area and inversely proportional to the distance between the plates. This means that increasing the area available for storing charge will result in a higher capacitance, as more charge can be accumulated on the plates for the same applied voltage.

Parallel Combination of Capacitors

When capacitors are connected in parallel, their overall capacitance is the sum of the individual capacitances. This occurs because each capacitor's plates contribute independently to the total charge storage, while the voltage across each capacitor remains the same. As a result, placing two identical capacitors in parallel gives a total capacitance that is twice the capacitance of one single capacitor.

Effective Area

The idea of effective area comes into play because when capacitors are placed in parallel, it is as if the plate area is increased. Each capacitor provides its own plate area for storing charge, and when combined, the total area available for charge storage doubles. This enlarged effective area directly leads to a doubling of the capacitance, assuming all other variables remain constant.

Charge Interaction in Capacitors

The behavior of electric charges on a capacitor is governed by the principle that like charges repel and opposite charges attract. In individual capacitors, this interaction ensures that the charge separation is maintained, establishing an electric field. When two capacitors are connected in parallel, these interactions still occur independently in each capacitor, but the net effect is an increased ability to accumulate charge over a larger effective area, reinforcing why the overall capacitance is doubled.

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