In a two-source circuit, one source acting alone produces 10 ma through a given branch. the other source acting alone produces 8 ma in the opposite direction through the same branch. the actual current through the branch is

Refer to the figure below.

R = resistance.

Case 1:

The voltage source is V₁ and the current is 10 mA. Therefore

V₁ = (10 mA) R

Case 2:

The voltage source is V₂ and the current is 8 mA. Therefore

V₂ = (8 mA) R

Case 3:

The voltage across the resistance is V₁ - V₂. Therefore the current I is given by

V₁ - V₂ = IR

10R - 8R = (I mA) R

2 = I

The current is 2 mA.

Answer: 2 mA