question_answer

Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:

When   some   potential   difference   is maintained between A and B, current i enters the network at A and leaves at B as shown in the figure. Then (1) The equivalent resistance between A and B is\[8\,\Omega \]. (2) C and D are at the same potential (3) Current\[\frac{3i}{5}\]flows from D to C (4) No current flows between C and D

A)  1, 2 and 3 are correct

B)  1 and 2 are correct

C)   2 and 4 are correct

D)  1 and 3 are correct

Correct Answer: A

Solution :

                 The equivalent resistance between points A and B is \[{{R}_{eq}}=\frac{20\times 5}{20+5}+\frac{5\times 20}{5+20}\] \[{{R}_{eq}}=8\,\Omega \] C and D are joined, they must be at the same potential. \[{{V}_{A}}-{{V}_{C}}={{V}_{A}}-{{V}_{D}}\] \[20{{i}_{1}}=5(i-{{i}_{1}})\] \[{{i}_{1}}=\frac{i}{5}\] Current flowing from D to C is                 \[i-2{{i}_{1}}=i-\frac{2i}{5}=\frac{3i}{5}\]                Hence, option  is correct.