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.