question_answer

The currents \[{{i}_{1}}\] and \[{{i}_{2}}\] through the resistors \[{{R}_{1}}(=10\,\Omega )\] and\[{{R}_{2}}(=30\,\Omega )\] in the circuit diagram with \[{{E}_{1}}=3V,\,{{E}_{2}}=3V\] and \[{{E}_{3}}=2\,V\] are respectively

A)  0.2 A, 0.1 A        

B)  0.4 A, 0.2 A

C)  0.1 A, 0.2 A        

D)  0.2 A, 0.4 A

Correct Answer: A

Solution :

                 In closed loop EFGDE \[{{i}_{2}}{{R}_{2}}={{E}_{2}}\] \[{{i}_{2}}\times 30=3\] In closed loop ABCEA \[-{{i}_{1}}{{R}_{1}}-{{E}_{1}}+{{E}_{2}}+{{E}_{3}}=0\] \[-{{i}_{1}}\times 10-3+3+2=0\]                 \[{{i}_{1}}=0.2A\]