question_answer

What will be the change in the resistance of a circuit consisting of five identical conductors if two similar conductors are added as shown by the dashed line in figure.

A) becomes 1/5 times         

B) becomes 3/5 times

C) becomes 2/5 times

D) becomes 1/2 times

Correct Answer: B

Solution :

[b] After adding two conductors, the circuit will acquire the form shown in figure. From symmetry considerations, we calculate that the central conductor will not participate in electric charge transfer. Therefore, if the initial resistance \[{{R}_{1}}\] of the circuit was 5r, where r is the resistance of a conductor, the new resistance of the circuit will become \[{{R}_{2}}=2r+\frac{2r}{2}=3r\text{  Therefore, }\frac{{{R}_{2}}}{{{R}_{1}}}\text{=}\frac{3}{5}\text{ }\]