Three parallel plate capacitors of capacitances $4 \mu \mathrm{~F}$, $6 \mu \mathrm{~F}$ and $12 \mu…

Three parallel plate capacitors of capacitances $4 \mu \mathrm{~F}$, $6 \mu \mathrm{~F}$ and $12 \mu \mathrm{~F}$ are first connected in series and then in parallel. The ratio of the effective capacitances in the two cases is
  1. $1: 11$
  2. $5: 8$
  3. $3: 7$
  4. $4: 9$

Solution

For parallel combination of capacitors, $C_p=C_1+C_2+C_3=4+6+12=22 \mu \mathrm{~F}$
For series combination of capacitors, $\begin{aligned} & \frac{1}{\mathrm{C}_5}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2}+\frac{1}{\mathrm{C}_3}=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}=\frac{1}{2} \\ & \therefore \mathrm{C}_5=2 \mu \mathrm{~F} \\ & \therefore \frac{\mathrm{C}_{\mathrm{s}}}{\mathrm{C}_{\mathrm{p}}}=\frac{2}{22}=1: 11 \end{aligned}$

Asked in: AP EAMCET 2024 (20 May Shift 2)

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