Question

Find the equivalent capacitance between the points $\text{A}$ and $\text{B}$ in the given circuit?

• A. $3\mu \text{F}$
• B. $7.5\mu \text{F}$
• C. $2.5\mu \text{F}$
• D. $5\mu \text{F}$

Answer 1

The correct option is C $2.5\mu \text{F}$

From the given figure we can see $C_2$ and $C_3$ are in series and their equivalent capacitance is parallel to $C_4$ .

Equivalent capacitance of $C_2$ and $C_3$,

$C_{23}=\frac{C_2{C}_3}{C_2+C_3}=\frac{6\times 3}{6+3}=\frac{18}{9}=2\mu \text{F}$

Now, $C_{23}$ and $C_4$ are in parallel, so their effective capacitance $C^{\prime \prime }$ as

$C^{\prime \prime }=2+3=5\mu \text{F}$


Now, $C_1$ and $C^{\prime \prime }$ are in series

$C_{eq}=\frac{C_1{C}^{\prime \prime }}{C_1+C^{\prime \prime }}=\frac{5\times 5}{5+5}=2.5\mu \text{F}$

Hence, option (c) is the correct answer.