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

Options

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

Answer

C

Explanation

The given circuit can be draw as

Applying kirchhoff's volatge 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
`-(i_(1) +i_(2))R - i_(i)r_(2) +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 equations.