The capacitance of two capacitors connected in parallel is four times their capacitance when they are connected in series. The ratio of their individual capacitances is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 1
In parallel the capacitances add, \( C_p=C_1+C_2 \). In series the reciprocals add, which for two capacitors gives \( C_s=C_1C_2/(C_1+C_2) \).
Putting \( C_p=4C_s \):
\( \displaystyle C_1+C_2=\frac{4C_1C_2}{C_1+C_2} \)
\( (C_1+C_2)^{2}=4C_1C_2 \)
\( C_1^{2}-2C_1C_2+C_2^{2}=0 \)
\( (C_1-C_2)^{2}=0 \)
\( \Rightarrow\; C_1=C_2 \)
Therefore, the two capacitances are equal, and \( C_1:C_2=1:1 \).