Assertion (A) Two condensers of same capacity are connected first in parallel and then in series. The ratio…
Assertion (A) Two condensers of same capacity are connected first in parallel and then in series. The ratio of resultant capacities in the two cases will be $4: 1$.
Reason ( $R$ ) In parallel, capacity increases and in series capacity decreases.
Both $A$ and $R$ are true and $R$ is a correct explanation for $\mathrm{A}$.
Both $A$ and $R$ are true but $R$ is not a correct explanation for A.
$A$ is true but $R$ is false.
$A$ is false but $R$ is true.
Solution
Given, two capacitors of same capacities $C$.
In series, equivalent capacitance is given by
$\begin{aligned} & \frac{1}{C_S}=\frac{1}{C_1}+\frac{1}{C_2}=\frac{1}{C}+\frac{1}{C}=\frac{2}{C} \\ & C_S=\frac{C}{2}\end{aligned}$
In parallel, equivalent capacitance is given by
$C_P=C_1+C_2=C+C=2 C$
Ratio $=\frac{C_P}{C_S}=\frac{2 C}{\left(\frac{C}{2}\right)}=\frac{4}{1}$
$\Rightarrow \quad C_P: C_S=4: 1$
Hence, Assertion is true
In parallel, $C_P>C$
In series, $C_S < C$
So, in parallel, capacity is increased but in series, capacity is decreased.
Hence, Reason is also true, but it is not the correct explanation of Assertion.