In the given circuit the current `I_(1)` is

Options

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

Answer

B

Explanation

(b) The circuit can be simplified as follows
Applying `KCL` at junction `A`
`i_(3) = i_(1) + i_(2)`
Applying Kirchhoff's voltage lawfor the loop `ABCDA`
`- 30i_(1) - 40 i_(3) + 40 = 0`
`implies - 30 i_(1) - 40 (i_(1) + i_(2)) + 40 = 0`
`implies 7 i_(1) + 4 i_(2) = 4`
Applying Kirchhoff's voltage law for the loop `ADEFA`.
`- 40 i_(2) - 40 i_(3) + 80 + 40 = 0`
`implies - 40 i_(2) - 40(i_(1) + i_(2)) = - 120`
`implies i_(1) + 2i_(2) = 3`
On solving equation (ii) and (iii) `i_(1) = - 0.44 A`.