Problem with variable capacitor and changing angles

In summary, the problem involves a variable capacitor with 7 armatures in the shape of half-circles with a radius of 2 cm and a distance of 1 mm separating them. The capacity needs to be found for three different angles, 0 degrees, 45 degrees, and 135 degrees. Relevant equations include C=Q/V and C=ε0 * A / d, where d is the distance between the armatures and ε0 is the constant of permitivity of empty space. The solution involves considering the effective area of the rotating and stationary plates and connecting them accordingly. The angle change will also affect the equations used.
  • #1
lesdavies123
16
0

Homework Statement



Here is the problem: A variable capacitor has seven armatures in the shape of half-circles with a radius of 2 cm. The armatures have a distance of 1 mm separating them. Find the capacity when the angle θ is: (a) 0 degrees; (b) 45 degrees; (c) 135 degrees.

Homework Equations



I guess relevant equations are C=Q/V and C=ε0 * A / d with d being the distance between the armatures. Also ε0 is the constant of permitivitty of empty space which is 8.85 x 10-12 F/m.


The Attempt at a Solution



Basically, I've done problems with capacitors with two armatures, but now there are 7, so I don't know how they are paired up. Usually, the area obtained is the area of one of the two armatures, so here would the area be that of only one armature or should we multiply it by 3.5 to have half the total area (I tried that, but it didn't work). Also, I don't know how the angle changing would be reflected in any equations or what effect it would have. A little help to get me started would make me very happy. Thank you!
 
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  • #2
There are 7 rotating and 8 stationary semicircular plates. The effective area is the part covering both the stationary and rotating plates.

All rotating plates connect to each other. All stationary plates connect to each other.
 

1. What is a variable capacitor?

A variable capacitor is an electronic component that allows for the adjustment of its capacitance (the ability to store electrical charge) by changing its physical dimensions or the distance between its plates.

2. What is the function of a variable capacitor?

A variable capacitor is primarily used to tune circuits or adjust the frequency of an electronic signal. It is also commonly used in analog radio receivers, where it helps to select the desired radio station.

3. What is the problem with variable capacitors and changing angles?

The problem with variable capacitors and changing angles is that the capacitance can vary as the plates move closer or further apart, causing the electronic circuit to become unstable or produce unwanted effects.

4. How can the problem with variable capacitors and changing angles be solved?

The problem can be solved by using a fixed capacitor instead of a variable one, or by using a multi-section variable capacitor with fixed plates to maintain a constant capacitance regardless of the angle. Another solution is to use a digital variable capacitor, which can be controlled electronically and does not rely on physical movement.

5. Are there any other potential issues with variable capacitors?

Yes, variable capacitors can also have issues with temperature changes, humidity, and aging, which can affect the capacitance and cause changes in the circuit's performance. It is important to carefully select and test variable capacitors for specific applications to ensure reliable performance.

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