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Seven capacitors, each of capacitance 2 microfarad, are to be connected to give a net capacitance of 10/11 microfarad. Which of the following arrangements achieves this?
- 5 in parallel and 2 in series
- 4 in parallel and 3 in series
- 3 in parallel and 4 in series
- 2 in parallel and 5 in series
Correct answer: 5 in parallel and 2 in series
Solution
5 capacitors in parallel: Cₚ = 5 * 2 = 10 microfarad. 2 capacitors in series: Cₛ = 2/2 = 1 microfarad. These two groups in series: 1/C_net = 1/10 + 1/1 = 1/10 + 10/10 = 11/10. C_net = 10/11 microfarad. Total capacitors used: 5 + 2 = 7. This matches.
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