Question

In the given electrical circuit, which one of the following equations is a correct equation?

• A. $E_2-i_2{r}_2-E_1-i_1{r}_1=0$
• B. $E_1-\left(i_1+i_2\right)R+i_1{r}_1=0$
• C. $E_1-\left(i_1+i_2\right)R-i_1{r}_1=0$
• D. $-E_1-\left(i_1+i_2\right)R+i_2{r}_2=0$

Answer 1

Answer: (C)

The given circuit can be drawn as

Applying Kirchhoff's voltage law $(KVL)$ in loop $ABCDA$ , we get
$-(i_1+i_2)R+E_2-i_2{r}_2=0...(i)$
Applying $KVL$ in loop $ABFEA$ , we get
$-\left(i_1+i_2\right)R-i_1{r}_1+E_1=0...(ii)$
Applying $KVL$ in loop $EFCDE$, we get
$-E_1+i_1{r}_1+E_2-i_2{r}_2=0...(iii)$
From the given options, only option (c) satisfies Eq. (ii), hence it is the correct equation.