question_answer

Current through wire XY of circuit shown is:

A)   1 A                            

B)  4 A

C)  2 A                             

D)  3 A

Correct Answer: C

Solution :

Let current through XY is \[{{i}_{3}}.\]Applying Kirchhoff?s law to loop (1) and (2) \[{{i}_{1}}+0\times {{i}_{3}}-3{{i}_{2}}=0\] \[{{i}_{1}}=3{{i}_{2}}\]                                                    (i) and \[-2({{i}_{1}}-{{i}_{3}})+4({{i}_{2}}+{{i}_{3}})=0\] So, \[2{{i}_{1}}-4{{i}_{2}}=6{{i}_{3}}\]                                    (ii) Also, \[50=1{{i}_{1}}-2(i-{{i}_{3}})\] \[\therefore \]    \[3{{i}_{1}}-2{{i}_{3}}=50\]                                 (iii) From Eqs. (i), (ii), and (iii),  we get \[{{i}_{2}}=2A\] Hence, the correction option is [c].