Question

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

• A. connecting them in series
• B. connecting them is parallel
• C. connecting two in series and one in parallel
• D. connecting two in parallel and one in series

Answer 1

Answer: (C)

connecting two in series and one in parallel

Three capacitors $C1=C2=C3=C=4\mu F$

The effective capacitance of the combination $Ceq=6\mu F$

$A)ConnectingC1,C2,C3inseries$

$Ceq=\frac{C}{3}=\frac{4}{3}\mu F$

$B)ConnectingC1,C2,C3inparallel$

$Ceq=C1+C2+C3=12\mu F$

$C)Connectingtwoinseriesandinparallel$

$Ceq=\frac{C1C2}{C1+C2}+C3=\frac{C}{2}+C=6\mu F$

$D)Connectingtwoinparallelandinseries$

$\frac{1}{Ceq}=\frac{1}{C1+C2}+\frac{1}{C3}$

$Ceq=2.67\mu F$

Thus only option $C$ is correct