Question

In the arrangement of capacitors shown in figure, each capacitor is of 9 μF, Then the equivalent capacitance between in points A and B is ---​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ All the capacitance are of equal values

✭ So C1 = C2 = C3 = C4 = 9 micro farad

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Equivalent capacitance between A & B?

$\displaystyle\large\underline{\sf\gray{Solution}}$

Check the attachment for a simplified diagram!!

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

Case 1

✭ $\displaystyle\sf C_1 \ \& \ C_3 \ are \ parallel$

➝ $\displaystyle\sf C_x = C_1+C_3$

➝ $\displaystyle\sf \purple{C_x = 18 \mu F}$

Case 2

✭ $\displaystyle\sf C_2 \ \& \ C_x \ are \ in \ series$

»» $\displaystyle\sf \dfrac{1}{C_y} = \dfrac{1}{C_2} + \dfrac{1}{C_x}$

»» $\displaystyle\sf \bigg\lgroup \dfrac{1}{9}+\dfrac{1}{18}\bigg\rgroup \bigg\lgroup \dfrac{1}{10^{-6}}\bigg\rgroup$

»» $\displaystyle\sf \bigg\lgroup\dfrac{2+1}{18} \bigg\rgroup\bigg\lgroup\dfrac{1}{10^{-6}}\bigg\rgroup$

»» $\displaystyle\sf \dfrac{1}{C_y} = \dfrac{3}{18}\times \dfrac{1}{10^{-6}}$

»» $\displaystyle\sf C_y = \dfrac{18}{3}\times 10^{-6}$

»» $\displaystyle\sf \orange{C_y = 6\mu F}$

Case 3

✭ $\displaystyle\sf C_y \ \& \ C_4 \ are \ parallel$

➳ $\displaystyle\sf C_R = C_y+C_4$

➳ $\displaystyle\sf (6+9)10^{-6}$

➳ $\displaystyle\sf \pink{C_R = 15\mu F}$

$\underline{\therefore\textsf{Resultant capacitance between A and B is 15 micro farad}}$

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Answer 2

$capacitor \: in \: parallel$

$c_{3} + c_{1} = 18fp = =c′$

$series$

$\frac{1}{c} = \frac{ 1}{ c′ } + \frac{1}{ c_{2} }$

$\frac{1}{18} + \frac{1}{9}$

$= \frac{1}{6}$

$c′ = 6pf$

$equivalent = (9 + 6)pf$

$= 15pf$