When the switch S, in the circuit shown, is closed, then the value of current i will be:

We will use the formula for current in terms of voltage and resistance to determine the current i. We'll allow node's potential to be X. The value of X will then be determined by entering the data from the question into the formula. please see the response below.

The voltage remain at $C=x V$
In Kirchhoff's present legal system,
$i_1+i_2=i$
$\Rightarrow \frac{20-x}{2}+\frac{10-x}{4}=\frac{x-0}{2}$
$\Rightarrow x=10$
$\therefore i=\frac{V}{R}=\frac{x}{R}=\frac{10}{2}=5 \mathrm{A}$

Hence, the correct answer is option B.