Question
See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it?
A.
$${\varepsilon _1} - \left( {{i_1} + {i_2}} \right)R - {i_1}{r_1} = 0$$
B.
$${\varepsilon _2} - {i_2}{r_2} - {\varepsilon _1} - {i_1}{r_1} = 0$$
C.
$$ - {\varepsilon _2} - \left( {{i_1} + {i_2}} \right)R + {i_2}{r_2} = 0$$
D.
$${\varepsilon _1} - \left( {{i_1} + {i_2}} \right)R + {i_1}{r_1} = 0$$
Answer :
$${\varepsilon _1} - \left( {{i_1} + {i_2}} \right)R - {i_1}{r_1} = 0$$
Solution :
The algebraic sum of the changes in potential in complete transversal of a mesh (closed loop) is zero. i.e. $$\Sigma V = 0$$
So, $${\varepsilon _1} - \left( {{i_1} + {i_2}} \right)R - {i_1}{r_1} = 0$$