Question

We wish to obtain a capacitance of $5\mu F$, by using some capacitors, each of $2\mu F$. Then, the minimum number of capacitors required is

• A. $3$
• B. $4$
• C. $5$
• D. $\text{Not possible}$

Answer 1

The correct option is B $4$

As we can only use 2 $\mu F$ capacitors to achieve the total capacitance of 5 $\mu F$. So, the best combination that can be made is
$5\mu F$ = $2\times 2\mu F+1\mu F$
For this, we need to connect two capacitors of 2 $\mu F$ each in parallel and connect another two capacitors of $2\mu F$ each in series and further connect both set in parallel to achieve the capacitance of $5\mu F$.
Its initial digramatic representation can be shown as

Upon further connecting all these capacitors in the systematic manner, the final circuit can be shown as below:
To acheive 1 $\mu F$ we need to connect 2 capacitors of 2 $\mu F$ each in series.
$\frac{1}{1\mu F}=\frac{1}{2\mu F}+\frac{1}{2\mu F}$
So, from the diagram above, we can say the minimum number of capacitors required to acheive the capacitance of $5\mu F$ is $4$.