question_answer

The currents ii and 13 through the resistors\[{{R}_{1}}(=10\,\Omega )\]and\[{{R}_{2}}(=30\,\Omega )\]in the circuit -diagram with\[{{E}_{1}}=3V\,,{{E}_{2}}=3V\]and\[{{E}_{3}}=2V\]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

E)  0.4 A, 0.1 A

Correct Answer: A

Solution :

In closed loop EFGDE                 \[{{i}_{2}}{{R}_{2}}={{E}_{2}}\]                 \[{{i}_{2}}\times 30=3\]                 \[{{i}_{2}}=0.1\,A\] In closed loop ABCEA                 \[-{{i}_{1}}{{R}_{1}}-{{E}_{1}}+{{E}_{2}}+{{E}_{3}}=0\]                 \[-{{i}_{1}}\times 10-3+3+2=0\]                 \[{{i}_{1}}=0.2A\]