question_answer

If each of the resistance of the network shown in figure is R, the equivalent resistance between A and B is:

A)  3R                         

B)  5R

C)  R/2                       

D)  R

Correct Answer: D

Solution :

\[{{i}_{1}}=0.9\,\text{amp}\text{.}\]       \[{{R}_{1}}=2\Omega \] \[E={{i}_{1}}{{R}_{1}}+{{i}_{1}}r\]                                              ?(i) \[{{R}_{2}}=7\Omega \,{{i}_{2}}=0.3\,\text{amp}\] \[E={{i}_{2}}{{R}_{2}}+r\,{{i}_{2}}\] \[E=0.3\times 7+0.3\,r\] Eq. (i) is equal to eq.(ii) \[0.9\times 2+0.9r=0.3\times 7+9.3r\] \[0.6r=2.1-1.8\] \[r=\frac{0.3}{0.6}\] \[=0.5\,\Omega \]