Question

Find the equivalent capacitance across A & B

• A. $\frac{28}{3}\mu f$
• B. $\frac{15}{2}\mu F$
• C. 15 mF
• D. none

Answer 1

The correct option is B $\frac{15}{2}\mu F$

The Capacitance $23\mu f$ and $12\mu f,1\mu f$ and $1\mu f$ are connected in paralled so their equivalent capacitance is : $(23+12)\mu f,(1+1)\mu f$ respectively i,e

$35\mu f$ and $2\mu f$

Now the whole circuit is in form of wheatsfftone bridge with :

$C_1=35\mu f,C_2=\mu f,C_3=10\mu f$ and $C_4=2\mu f$

Clearly, $\frac{C_1}{C_2}=\frac{C_3}{C_4}=5$

So $13\mu f$ capacitor is neglected

Now equivalent capacitance of $C_1$ and $C_2$ in series = $\frac{C_1{C}_2}{C_1+C_2}\mu f$

Equivalent capacitance of $C_3$ and $C_4$ in series = $\frac{10\times 2}{10+2}=\frac{20}{12}$$\mu f$

Now these two equivalent capacitances are connected in parallel so their equivalent is :

$C_{eq}=\frac{245}{42}+\frac{20}{12}=\frac{15}{2}\mu f$