Question

Three capacitors each of $4\mu F$ are to be connected in such a way that the effective capacitance is $6\mu F$. This can be done by connecting them:

• A. all in parallel
• B. two in parallel and one in series
• C. all in series
• D. two in series and one in parallel

Answer 1

Answer: (D)

For capacitor is series, equivalent capacitance is given by:

$C_S=\frac{C_1{C}_2}{C_1+C_2}$

For capacitor is parallel, equivalent capacitance is given by:

$C_P=C_1+C_2$

In the given configuration, equivalent capacitance is given by

$C_{eq}=C_s+C$, where $C=4\mu F$

and $C_s=\frac{C\times C}{C+C}=\frac{C}{2}$

$\therefore C_{eq}=C+\frac{C}{2}=6\mu F$