question_answer

For the current loops shown in the figure, Kirchhoffs loop rule for the loops AHDCBA and AHDEFGA yields these equations respectively

A)  \[-30{{I}_{1}}-41{{I}_{3}}+45=0\,\,and\,-30A{{I}_{1}}\] \[+21{{I}_{2}}-80=0\]

B)                  \[30{{I}_{1}}-41{{I}_{3}}+45=0\,\,and\]\[30{{I}_{1}}-21{{I}_{2}}-80=0\]

C)  \[30{{I}_{1}}+41{{I}_{3}}-45=0\,\,and\,\]\[-30{{I}_{1}}+21{{I}_{3}}+80=0\,\,\]

D)  None of the above

Correct Answer: D

Solution :

                 Applying Kirchhoffs loop rule for the closed loop AHDCBA                                 \[-30{{I}_{1}}-45-40{{I}_{3}}-{{I}_{3}}=0\]                     \[-30{{I}_{1}}-45-41{{I}_{3}}=0\] Applying Kirchhoffs loop rule for closed loop AHDEFGA                 \[-30{{I}_{1}}+20{{I}_{2}}+{{I}_{2}}-80=0\]                      \[-30{{I}_{1}}+21{{I}_{2}}-80=0\] So, option  is correct.