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.
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 CBC = CB + CC, and CDE = CD + CE. And then CEQ = 1/(1/CA + 1/CBC + 1/CDE + 1/CF) (since I considered these to be in series). Capacitance of a sphere is C = 4πεOR. So using this approach, I found CEQ = (90/133)( 4πεOR). Do I have the right idea, or am I way off?
12.7 KB Views: 534