Question

If a battery is placed between $\text{A}$ and $\text{B}$, with what capacitor you can replace the combination of the given capacitors ?

• A. $8\mu \text{F}$
  
• B. $6\mu \text{F}$
• C. $26\mu \text{F}$
• D. $\frac{10}{3}\mu \text{F}$
  

Answer 1

The correct option is A $8\mu \text{F}$


As we can see from the circuit, the capacitors present in the top branch are in series, and also the capacitors in bottom branch are in series.

Since, the capacitance of the capacitors are same so, the equivalent capacitance of the top branch and bottom branch will be same as,

$C_{top}=C_{bottom}=\frac{4\times 4}{4+4}=2\mu \text{F}$


Now, all the three branches are in parallel, so the equivalent capacitance across $\text{AB}$

$C_{equ}=2\mu \text{F}+4\mu \text{F}+2\mu \text{F}$

$\therefore C_{equ}=8\mu F$

Hence, option (a) is the correct answer.