Question

What is the equivalent capacitance of the system of capacitors between $\text{A}$ and $\text{B}$

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

Answer 1

The correct option is B

$1.6C$
Let arrange the circuit as shown in figure, using

$C_{eq}=\frac{C_1{C}_2}{C_1+C_2}$ $\text{for series}$

$C_{eq}=C_1+C_2\text{for parallel}$

Equivalent capacitance between $2$ and $\text{B}$

$C_{2B}=\frac{C\times C}{C+C}=\frac{C}{2}$


Equivalent capacitance between $1$ and $\text{B}$,

$C_{1B}=C_{13}+C_{2B}=C+\frac{C}{2}=\frac{3C}{2}$




Equivalent capacitance between $\text{A},1$ and $\text{B}$,
$C_{A1B}=\frac{C\times \frac{3C}{2}}{C+\frac{3C}{2}}=\frac{3C}{5}$



Now, equivalent capacitance between $\text{A}$ and $\text{B}$,

$C_{AB}=C+\frac{3C}{5}=1.6C$

Hence, option (b) is correct answer.