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In the arrangement of the capacitors as shown in figure, each capacitor is of $6 \mu \mathrm{F}$, then equivalent capacity between points $\mathrm{A}$ and $B$ is
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Verified Answer
The correct answer is:
$10 \mu \mathrm{F}$
$\mathrm{C}_1$ and $\mathrm{C}_3$ are in parallel.
Hence their equivalent capacitance $\mathrm{C}_5=2 \times 6=12 \mu \mathrm{F}$
$\mathrm{C}_5$ and $\mathrm{C}_2$ in series. Hence their equivalent capacitance $\mathrm{C}_6$ is given by
$$
\frac{1}{\mathrm{C}_6}=\frac{1}{12}+\frac{1}{6}=\frac{3}{12}=\frac{1}{4}
$$
$\therefore \mathrm{C}_6$ and $\mathrm{C}_4$ are in parallel.
Hence their equivalent capacitance is $\mathrm{C}=4+6=10 \mu \mathrm{F}$
Hence their equivalent capacitance $\mathrm{C}_5=2 \times 6=12 \mu \mathrm{F}$
$\mathrm{C}_5$ and $\mathrm{C}_2$ in series. Hence their equivalent capacitance $\mathrm{C}_6$ is given by
$$
\frac{1}{\mathrm{C}_6}=\frac{1}{12}+\frac{1}{6}=\frac{3}{12}=\frac{1}{4}
$$
$\therefore \mathrm{C}_6$ and $\mathrm{C}_4$ are in parallel.
Hence their equivalent capacitance is $\mathrm{C}=4+6=10 \mu \mathrm{F}$
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