AP EAMCET · PHYSICS · Capacitance
If 27 indentical charged conducting spheres each of capacitance \(10 \mu \mathrm{~F}\) combine to form a big sphere, then the capacitance of the big sphere is
- A \(30 \mu \mathrm{~F}\)
- B \(270 \mu \mathrm{~F}\)
- C \(90 \mu \mathrm{~F}\)
- D \(10 \mu \mathrm{~F}\)
Answer & Solution
Correct Answer
(A) \(30 \mu \mathrm{~F}\)
Step-by-step Solution
Detailed explanation
\(R_{\text{big}} = (27)^{1/3} R_{\text{small}} = 3 R_{\text{small}}\) \(C_{\text{big}} = 3 C_{\text{small}}\) \(C_{\text{big}} = 3 \times 10 \, \mu\mathrm{F} = 30 \, \mu\mathrm{F}\)
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