question_answer

In the given circuit the current I1 is                           [DCE 2000]

A)            0.4 A

B)            ? 0.4 A

C)            0.8 A

D)            ? 0.8 A

Correct Answer: B

Solution :

           The circuit can be simplified as follows Applying KCL at junction A \[{{i}_{3}}={{i}_{1}}+{{i}_{2}}\]         .?.(i) Applying Kirchoff?s voltage law for the loop ABCDA        \[-30{{i}_{1}}-40{{i}_{3}}+40=0\] \[\Rightarrow \,\,\,\,\,\,-30{{i}_{1}}-40({{i}_{1}}+{{i}_{2}})+40=0\] \[\Rightarrow \,\,\,\,\,\,\,7{{i}_{1}}+4{{i}_{2}}=4\]                            .?.(ii) Applying Kirchoff?s voltage law for the loop ADEFA. \[-40{{i}_{2}}-40{{i}_{3}}+80+40=0\]                                                        \[\Rightarrow \,\,\,\,\,-40{{i}_{2}}-40({{i}_{1}}+{{i}_{2}})=-120\] \[\Rightarrow \,\,\,\,\,\,{{i}_{1}}+2{{i}_{2}}=3\,\]                              ??.(iii) On solving equation (ii) and (iii) \[{{i}_{1}}=-0.4A\].