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Homework Statement
Figure P26.26 shows six concentric conducting spheres, A, B, C, D, E, and F having radii R, 2R, 3R, 4R, 5R, and 6R, respectively. Spheres B and C are connected by a conducting wire, as are spheres D and E. Determine the equivalent capacitance of this system.
Homework Equations
Capacitance of a sphere: C = 4pi(epsilon0)R
Capacitance in general: C = Q/V
The Attempt at a Solution
I’m supposed to find the equivalent capacitance of this arrangement. I was kind of perplexed by this one. But here’s what I’ve been thinking. OK. B and C are at the same potential (because they're connected by a wire). D and E are also at the same potential. So it’s like B and C are in parallel, as are D and E. So I said C_{BC} = C_{B} + C_{C}, and C_{DE} = C_{D} + C_{E}. And then C_{EQ} = 1/(1/C_{A} + 1/C_{BC} + 1/C_{DE} + 1/C_{F}) (since I considered these to be in series). Capacitance of a sphere is C = 4πε_{O}R. So using this approach, I found C_{EQ} = (90/133)( 4πε_{O}R). Do I have the right idea, or am I way off?
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