Question

Three capacitors 4 uF, 6 uF and 12 uF are connected in series and then in
parallel. What is the ratio of their equivalent capacitances in two cases (Cs:
Cp)?​

Answer 1

Answer:

hope you got your answer

Answer 2

Given :

⟶ Three identical capacitors of capacitance 4uF, 6uF and 12uF are connected in

1. series
2. Parallel

To Find :

➳ Ratio of their equivalent capacitance in two cases.

SoluTion :

✴ Eq. of series connection :

$\dashrightarrow\tt\:\dfrac{1}{C_s}=\dfrac{1}{C_1}+\dfrac{1}{C_2}+\dfrac{1}{C_3}\\ \\ \dashrightarrow\tt\:\dfrac{1}{C_s}=\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{12}\\ \\ \dashrightarrow\tt\:\dfrac{1}{C_s}=\dfrac{6+4+2}{24}\\ \\ \dashrightarrow\tt\:C_s=\dfrac{24}{12}\\ \\ \dashrightarrow\bf\:C_s=2\:uF\:\longrightarrow\:(i)$

✴ Eq. of parallel connection :

$\implies\tt\:C_p=C_1+C_2+C_3\\ \\ \implies\tt\:C_p=4+6+12\\ \\ \implies\bf\:C_p=22\:uF\:\longrightarrow\:(ii)$

✭ Taking ratio of (i) & (ii), we get

$\mapsto\tt\:\dfrac{C_s}{C_p}=\dfrac{2}{22}\\ \\ \mapsto\underline{\boxed{\bf{C_s:C_p=1:11}}}\:\gray{\bigstar}$