Question

What is the equivalent capacitance of the system of capacitors shown in the figure below between points $\text{A}\&\text{B}$

• A. $\frac{7C}{6}$
• B. $1.6C$
• C. $C$
• D. None

Answer 1

The correct option is B $1.6C$

The given circuit is


Equivalent capacitance between $\text{x}$ and $\text{B}$

$C^{\prime }=\frac{C\times C}{C+C}=\frac{C}{2}$


Now, Equivalent capacitance between $\text{x}$ and $\text{B}$

$C^{\prime \prime }=\frac{C}{2}+C=\frac{3C}{2}$


Equivalent capacitance of $C$ and $\frac{3C}{2}$
$C^{\prime \prime \prime }=\frac{\frac{\frac{3C}{2}\times C}{3C}}{2}+C=\frac{3C}{5}$


Now the equivalent of capacitance between $A$ and $B$
$C_{eq}=\frac{3C}{5}+C=\frac{8C}{5}$

Therefore , Resultant capacitance of the circuit is $1.6C$

Hence, option (b) is the correct answer.