At the node picture below, i1 = 5 A, i2 = -1 A and i3 = 3 A. Find ix in Amps.

Question

BlackTom AI · Accepted Answer

Kirchhoff’s Current Law (KCL) — the algebraic sum of currents at a node equals zero — is the key concept. Treat currents leaving the node as positive and entering as negative (or write entering = leaving). Here the arrows show i1, i2 and i3 leaving the node and ix entering from the right, but the given sign for i2 can reverse its actual direction.

1) Relevant knowledge points and concepts
- KCL: sum of currents into a node = sum of currents out of the node (equivalently the algebraic sum = 0).
- Pay attention to sign: a negative numeric current means the actual direction is opposite the arrow shown.

2) Complete reasoning process step by step
- Write KCL with leaving currents positive: i1 + i2 + i3 − ix = 0 (since ix arrow points toward the node, it is entering).
- Rearrange to solve for ix: ix = i1 + i2 + i3.

3) Calculations with intermediate steps
- Substitute the given values: i1 = 5 A, i2 = −1 A, i3 = 3 A.
- ix = 5 + (−1) + 3
- ix = 5 − 1 + 3
- ix = 4 + 3
- ix = 7 A

4) Why the correct answer is correct
- The algebraic sum correctly accounts for i2 being −1 A (meaning 1 A actually enters from the top). Summing the three algebraic values gives the net current entering from the right required to satisfy KCL.

5) Why other interpretations are incorrect (brief)
- Ignoring the negative sign on i2 would give ix = 5 + 1 + 3 = 9 A (wrong).
- Using the opposite sign convention without adjusting i2 would produce ix = −7 A or other sign errors. The correct algebraic handling of i2 yields 7 A.

6) Conclusion
- The computed current ix is 7 A, which matches the provided answer.

At the node picture below, i1 = 5 A, i2 = -1 A and i3 = 3 A. Find ix in Amps.数值题

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