What is the value of the current `I_(1)` in the given circuit ?

Options

A. 0.4A
B. `-0.4A`
C. 0.8A
D. `-0.8A`

Answer

B

Explanation

Applying Kirchhoff's voltage law to the loop ABDCA, we get
`-30I_(1)+40-40I_(3)=0`
But at point `C, I_(3)=I_(1)+I_(2)`
`therefore -30I_(1)+40-40 (I_(1)+I_(2)) therefore -70I_(1)-40I_(2)= -40`
`therefore 7I_(1)+4I_(2)=4`
Similarly for the loop, DCEFD,
`40-40I_(3)-40I_(2)+80=0`
`therefore 120-40(I_(1)+I_(2))-40I_(2)=0`
`120 =40I_(1)+80I_(2) therefore I_(1)+2I_(2)=3`
Multiplying (2) by (2), we get
`2I_(1)+4I_(2)=6`
`therefore` Subtracting (3) from (I), we get `5I_(1)= -2`
`therefore I_(1)= -(2)/(5)= - 0.4 A`