question_answer

Consider the electrical circuit Which equation for the circuit is correct?

A)  \[{{\varepsilon }_{1}}-({{L}_{1}}+{{L}_{2}})R+{{L}_{1}}{{r}_{1}}=0\]

B)  \[-{{\varepsilon }_{2}}-({{L}_{1}}+{{L}_{2}})R+{{i}_{2}}{{r}_{2}}=0\]

C)  \[{{\varepsilon }_{2}}-{{i}_{2}}{{r}_{2}}-{{\varepsilon }_{1}}-{{i}_{1}}{{r}_{1}}=0\]

D)  \[{{\varepsilon }_{1}}-({{i}_{1}}+{{i}_{2}})R-{{i}_{1}}{{r}_{1}}=0\]

Correct Answer: D

Solution :

                The circuit can re drawn as For loop - I (upper loop) Applying KVL,\[{{E}_{1}}-({{i}_{1}}+{{i}_{2}})R-{{i}_{1}}{{r}_{1}}=0\]