Loaded Divider KCL Three-Row Scan - Electronic Circuits II & III: Decision Networks and Interfaces Step by Step

At the loaded output node, the incoming source current splits exactly into the bottom-branch current and the load-branch current, and KCL must close for every row. The three rows give source currents of 2, 12/5, and 8/3 A as the sum of their two branch currents exactly for the ideal node model; real nodes add resistor tolerance, source impedance, loading, contact resistance, heating, supply limits, temperature drift, and current measurement uncertainty.

The output node current split closes by exact KCL for every load row. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The output node is a current-sum checkpoint

At the loaded output node, source current splits into bottom current and load current. The helper checks that split before the diagram is rendered.

I_s=I_b+I_L

Every row closes the node current sum

The source current column equals the bottom-branch current plus the load-branch current in each row.

\begin{array}{c|c|c}I_b&I_L&I_s\\1\ \text{A}&1\ \text{A}&2\ \text{A}\\\tfrac{4}{5}\ \text{A}&\tfrac{8}{5}\ \text{A}&\tfrac{12}{5}\ \text{A}\\\tfrac{2}{3}\ \text{A}&2\ \text{A}&\tfrac{8}{3}\ \text{A}\\\end{array}

The first row splits two amperes into one plus one

For the rendered row, the source current is 2 amperes, and the two outgoing branch currents are each 1 ampere.

1\ \text{A}+1\ \text{A}=2\ \text{A}