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(D) Applying Kirchhoff's voltage law to the loop $ABFE$ in the clockwise direction:Starting from point $A$ and moving towards $B$,the potential drop a

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$E_1 - (i_1 + i_2)R - i_1r_1 = 0$

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(D) Applying Kirchhoff's voltage law to the loop $ABFE$ in the clockwise direction:Starting from point $A$ and moving towards $B$,the potential drop across resistor $R$ is $-(i_1 + i_2)R$.Moving from $F$ to $E$ through the branch containing $E_1$ and $r_1$,we encounter the negative terminal of the battery first,so we add $E_1$,and the potential drop across $r_1$ is $-i_1r_1$.Equating the sum of potential changes to zero,we get:$-(i_1 + i_2)R - i_1r_1 + E_1 = 0$Rearranging the terms,we get:$E_1 - (i_1 + i_2)R - i_1r_1 = 0$

See the electrical circuit shown in the adjoining figure. Which of the following equations is a correct equation for it?

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