MCQ
Find the equivalent capacitance of the circuit between point $A$ and $B$.
- A$\frac{C}{3}$
- B$\frac{C}{8}$
- ✓$C$
- D$\frac{C}{32}$
✓
Answer
Correct option: C.
$C$
c
All the vertical capacitors are in between equal potential points i.e. a and b are equipotential points
All the vertical capacitors are in between equal potential points i.e. a and b are equipotential points
So we can remove all of these
For one series
$\frac{1}{C_{e q}}=\frac{1}{C}+\frac{1}{2 C}+\frac{1}{4 C}+\frac{1}{8 C}+\ldots$
$=\frac{1}{C}\left(1+\frac{1}{2}+\frac{1}{4}+\ldots .\right)$
$=\frac{1}{C} \times \frac{1}{1-\frac{1}{2}}=\frac{2}{C}=\left(S_{\infty}=\frac{1}{1-r}\right)$
$\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{\mathrm{C}}{2}$
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