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2. Electric potential and capacitance — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics2. Electric potential and capacitance1 Mark
MCQ
Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance $C$ if the equivalent capacitance between point $A$ and $B$ is to be $1\,\mu F$ is 
  • ✓
    $\frac{{32}}{{23}}\,\mu F$
  • B
    $\frac{{31}}{{23}}\,\mu F$
  • C
    $\frac{{33}}{{23}}\,\mu F$
  • D
    $\frac{{34}}{{23}}\,\mu F$
✓

Answer

Correct option: A.
$\frac{{32}}{{23}}\,\mu F$
a
Capacitors $2\, \mu \mathrm{F}$ and $2\, \mu \mathrm{F}$ are parallel, their equivalent $=4\, \mu \mathrm{F}$

$6 \,\mu \mathrm{F}$ and $12\, \mu \mathrm{F}$ are in series, their equivalent $=4\, \mu \mathrm{F}$

Now $4 \,\mu F(2 \text { and } 2\, \mu F)$ and $8\, \mu F$ in series

$=\frac{3}{8}\, \mu F$

And $4\, \mu \mathrm{F}(12 \& 6\, \mu \mathrm{F})$ and $4\, \mu \mathrm{F}$ in parallel $=4+4=8\, \mu \mathrm{F}$

$8\, \mu \mathrm{F}$ in series with $1\, \mu \mathrm{F}=\frac{1}{8}+1 \Rightarrow \frac{8}{9}\, \mu \mathrm{F}$

Now $C_{e q}=\frac{8}{9}+\frac{8}{3}=\frac{32}{9}$

$C_{eq}$ of circuit $=\frac{32}{9}$

With $C-\frac{1}{C_{e q}}=\frac{1}{C}+\frac{9}{32}=1 \Rightarrow C=\frac{32}{23}$

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