# In the circuit shown, if a wire is connected between points A and B, how much current will flow through it?

$\begin {array} {1 1} (A)\;5A & \quad (B)\;\large\frac{10}{3}A \\ (C)\;\large\frac{20}{3}A & \quad (D)\;\large\frac{5}{3}A \end {array}$

This question can be solved without much calculation. If A and B are connected,
then by the symmetry of the circuit, one can say that the current going through the $12\: ohm$
resistor on the left is the same as the current going out through the $12\: ohm$ resistor on the right.
Similarly is the case for the $6\: ohm$ resistor. Hence, there exist two current channels,
one of $24\: ohms$ and the other of $12\: ohms$. Hence the current is divided in $1:2$ ratio.
Effective resistance with A and B shorted is $8\: ohms$. Total current is $10A$.
Hence the current through the shorting wire is $\large\frac{10}{3}$$A$.
Ans : (B)
edited Mar 14, 2014
Can you please explain to me in detail that after finding the total current =10A,how the current through the shorting wire is 10/3A?