Solving Spherical Capacitors: Find C1 & C2 in Parallel

In summary, a spherical capacitor is an electrical component consisting of two concentric spherical conductors separated by an insulating material. The outer sphere is positively charged while the inner sphere is negatively charged. The capacitance of a spherical capacitor can be calculated using the formula C = 4πε₀ab/(a-b). When two capacitors are connected in parallel, the equivalent capacitance can be found by adding the individual capacitances. To find the individual capacitances, rearrange the equation Ceq = C1 + C2 to solve for C1 or C2. When solving for the capacitances of spherical capacitors in parallel, it is important to properly label the spheres and add the capacitances in the correct order, and to convert
  • #1
unscientific
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Homework Statement



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Homework Equations





The Attempt at a Solution



Working backwards I found that adding C1 (of radius a and b) and C2 (of radius b and c) in parallel gives the answer. Not sure why they can be modeled as capacitors in parallel though..
 
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  • #2
Consider the inner sphere and the inner surface of the middle shell as one capacitor, (blue) and the outer surface of the middle shell and the outer shell as the other one (yellow). A and G are the terminals of the resultant capacitor.
How are the capacitors connected? ehild
 

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What is a spherical capacitor and how does it work?

A spherical capacitor is a type of capacitor that consists of two concentric spherical conductors separated by an insulating material. The outer sphere is positively charged and the inner sphere is negatively charged. The insulating material, or dielectric, helps to maintain the separation of charges and allows for the storage of electrical energy.

How do you calculate the capacitance of a spherical capacitor?

The capacitance of a spherical capacitor can be calculated using the formula C = 4πε₀ab/(a-b), where ε₀ is the permittivity of free space, a is the radius of the outer sphere, and b is the radius of the inner sphere.

What is the equation for calculating the equivalent capacitance of two capacitors in parallel?

The equivalent capacitance of two capacitors in parallel can be calculated using the formula Ceq = C1 + C2, where C1 and C2 are the individual capacitances of the two capacitors.

How can I find the individual capacitances of two capacitors in parallel if the equivalent capacitance is known?

To find the individual capacitances of two capacitors in parallel, you can rearrange the equation Ceq = C1 + C2 to solve for C1 or C2. For example, C1 = Ceq - C2.

Are there any special considerations when solving for the capacitances of spherical capacitors in parallel?

Yes, when solving for the capacitances of spherical capacitors in parallel, it is important to make sure that the outer spheres and inner spheres are properly labeled and that the capacitances are added together in the correct order. It may also be necessary to convert units to ensure consistency.

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