Two capacitors, each of capacitance 2 F are connected in series and then in parallel. The ratio of equivalent capacitances in series to parallel combination is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1:4
Capacitors in series add as reciprocals, and capacitors in parallel add directly.
\( \displaystyle \frac{1}{C_s} = \frac{1}{2\,\mathrm{F}} + \frac{1}{2\,\mathrm{F}} \;\Rightarrow\; C_s = 1\,\mathrm{F} \)
\( C_p = 2\,\mathrm{F} + 2\,\mathrm{F} = 4\,\mathrm{F} \)
\( C_s : C_p = 1 : 4 \)
Shortcut: For n identical capacitors, \( C_s = C/n \) and \( C_p = nC \), so \( C_s : C_p = 1 : n^{2} \); with n = 2 this is 1 : 4.