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

Options

A. `E_(1) - (i_(1) + I_(2)) R- i_(1)r_(1) =0`
B. `E_(2) - i_(2)r_(2) - E_(1) - i_(1)r_(1)=0`
C. `-E_(2) - (i_(1) + i_(2))R + i_(2)r_(2)=0`
D. `E_(1) - (i_(1) + i_(2))R + i_(2)r_(2)=0`

Answer

A

Explanation

Loop BCDEB
`E_(1) - (i_(1) + i_(2)) R - i_(1)r_(1) = 0`
Loop ABEFA
`-E_(1) + i_(1)r_(1) + E_(2) - i_(2)r_(2) =0`
`rArr E_(2) - E_(1) + i_(1)r_(1) - i_(2)r_(2) = 0`
Loop ACDFA
`-(i_(1) + i_(2)) R + E_(2) -i_(2)r_(2) = 0`
`rArr (i_(1) + i_(2)) R - E_(2) + i_(2) r_(2) = 0`