The Answer: Solutions to Array of Capacitors Homework

In summary, an infinite array of identical 1-microFarad capacitors are arranged in a grid setup, where junctions are between capacitors, and each junction is connected to 4 other junctions separated by another capacitor. The array is initially uncharged and a battery is connected across two distant junctions. It can be shown that the potential at any junction is the average of the potential at the four nearest junctions by considering the net charge on any junction and using the equation V=Q/C. A figure is not provided, but the junctions are assumed to be the intersection points and the capacitors are all the same.
  • #1
GrantB
22
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Homework Statement



An infinite array of identical 1-microFarad capacitors are arranged in a grid setup, where junctions are between capacitors, and each junction is connected to 4 other junctions separated by another capacitor.

The array is initially uncharged. A battery is connected across two distant junctions.

Show that the potential at any junction is the average of the potential at the four nearest junctions.

(Hint: What is the net charge on any junction)

Homework Equations



V = Q/C
 
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  • #2
Any chance that you could provide a figure. Perhaps you could scan one.
 
  • #3
Sorry, I can't scan so I sloppily put together a picture:

http://imgur.com/k61zz

I'm assuming the junctions are the intersection points. All capacitors are the same.

EDIT: Also, it extends to infinity in every direction.
 

1. What is an array of capacitors?

An array of capacitors is a collection of two or more capacitors that are connected together in a circuit. This allows for a larger capacitance, which is the ability to store electrical charge, than a single capacitor alone.

2. How do you calculate the total capacitance of an array of capacitors?

The total capacitance of an array of capacitors can be calculated by adding the individual capacitances of each capacitor in series or by combining the individual capacitances in parallel using the appropriate formulas.

3. What is the difference between series and parallel connections in an array of capacitors?

In a series connection, the capacitors are connected end to end, creating a single path for the current to flow through. In a parallel connection, the capacitors are connected side by side, creating multiple paths for the current to flow through. This results in different total capacitances for each type of connection.

4. How does the voltage affect an array of capacitors?

The voltage affects an array of capacitors by determining the amount of charge that each capacitor can hold. A higher voltage will result in a larger charge stored in each capacitor, while a lower voltage will result in a smaller charge stored.

5. What are some practical applications of an array of capacitors?

An array of capacitors has many practical applications, including power factor correction, energy storage, and filtering in electronic circuits. They are also commonly used in camera flashes, power supplies, and audio equipment.

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