Superposition in a two-source network: One source alone drives 12 mA through a branch; the other source alone drives 10 mA in the opposite direction through the same branch. What is the actual branch current with both sources active?

Introduction / Context:
Linear circuit analysis often leverages superposition: the total response equals the algebraic sum of individual responses to each independent source acting alone (with the others turned off appropriately). Direction matters; currents opposing each other subtract.

Given Data / Assumptions:

• Current due to source 1 alone: I1 = 12 mA (reference direction taken as positive).
• Current due to source 2 alone: I2 = 10 mA in the opposite direction (hence negative with respect to the same reference).
• Linear network; sources are independent; superposition valid.

Concept / Approach:

Superposition principle: I_total = I1 + I2, with signs assigned according to direction. Opposite directions imply subtraction of magnitudes.

Step-by-Step Solution:

Verification / Alternative check:

Check limits: If both contributed in the same direction, magnitude would be 22 mA. With opposite directions and larger 12 mA, the remainder must be 2 mA, consistent with the arithmetic.

Why Other Options Are Wrong:

22 mA wrongly adds opposing currents. 12 mA or 10 mA ignores the second source. 0 mA would require equal magnitudes, which is not the case here.

Common Pitfalls:

Forgetting to treat direction as sign, or mixing up which direction is taken as positive.

Final Answer:

2 mA