For a two-source network, if current produced by one source is in one direction, while the current produced by the other source is in the opposite direction through the same resistor, the resulting current is? a. The product of the two and the direction of the smaller b. The difference between the two and has the same direction. c. The sum of the two and the direction of either d. The average of the two and the direction of the largest

c. The sum of the two and the direction of either.

Explanation:

If both sources are linear, we can apply the superposition theorem, which in this case, states simply that the resulting current is just the algebraic sum of both currents.

This is due to any of them, is independent from the other, so we can calculate her influence without any other source present.

Assuming that both sources are ideal (no shunt resistances), we can apply superposition, removing all sources but one each time, just replacing the sources by an open circuit.

Let's suppose that we have a 5A source flowing to the rigth, and a 3A source in the opposite direction.

Applying superposition, we have:

I₁ = 5A (the another source is removed)

I₂ = - 3A (The minus sign indicates that is flowing in the opposite direction, 5A source is removed)

I = I₁ + I₂ = 5A + (-3A) = 2 A

As it can be seen, the resulting current is the sum (algebraic) of both current sources, and has the direction of either of the sources, depending on the absolute value of the current sources.

(If the directions of I₁ and I₂ were inverted, with the same absolute values, the direction would be the opposite).

We could have arrived to the same result applying KCL.