Question

In the circuit shown in the figure, $C1=C,C_2=2C,C_3=3C,C_4=4C$. Then, select the incorrect statement(s) from the following.

• A. Maximum potential difference is across $C_1$
• B. Minimum potential difference is across combination of $C_3$ and $C_4$
• C. Maximum potential energy is in $C_1$
• D. Minimum potential energy is in $C_2$

Answer 1

The correct option is D Minimum potential energy is in $C_2$

Using the laws for series combination and parallel combination of capacitors,

$\frac{1}{C_{net}}=\frac{1}{C}+\frac{1}{2C}+\frac{1}{(3C+4C)}$

$\frac{1}{C_{net}}=23/14C\Rightarrow C_{net}=14C/23$

Charge provided by battery $=14CV/23$

Therefore,

potential across $C_1\left(C\right)=14V/23$

potential across $C_2\left(2C\right)=7V/23$

potential across $C_3$ and $C_4=2V/23$

also,

PE of $C_1\left(C\right)=2C{V}^2\times (7/23{)}^2$

PE of $C_2\left(2C\right)=C{V}^2\times (7/23{)}^2$

PE of $C_3\left(3C\right)=6C{V}^2/{23}^2$

PE of $C_4\left(4C\right)=8C{V}^2/{23}^2$