Loaded Divider Threshold Margin - Electronic Circuits II Step by Step

A loaded divider must compute the output node before comparing it to a threshold. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A load changes the lower divider branch

The source and divider resistors stay fixed. Only the load resistance changes, so every output shift comes from the same topology rule.

R_{\text{lower}}=R_b\parallel R_L,\quad V_o=I_sR_{\text{lower}}

Smaller loads pull the output closer to the threshold

Read the table left to right: the load changes the parallel lower resistance, then the source current, then the output voltage.

\begin{array}{c|c|c|c}R_L&R_b\parallel R_L&I_s&V_o\\12\ \text{ohm}&4\ \text{ohm}&\tfrac{12}{7}\ \text{A}&\tfrac{48}{7}\ \text{V}\\6\ \text{ohm}&3\ \text{ohm}&2\ \text{A}&6\ \text{V}\\3\ \text{ohm}&2\ \text{ohm}&\tfrac{12}{5}\ \text{A}&\tfrac{24}{5}\ \text{V}\\\end{array}

The same threshold receives three exact outputs

The threshold is fixed. Two rows remain above it; the smaller load row falls below it. The decision is the result of the comparison, not a hand-written label.

\begin{array}{c|c|c}V_o&V_{\text{threshold}}&\text{decision}\\\tfrac{48}{7}\ \text{V}&5\ \text{V}&HIGH\\6\ \text{V}&5\ \text{V}&HIGH\\\tfrac{24}{5}\ \text{V}&5\ \text{V}&LOW\\\end{array}

The rendered row closes current and threshold

For the rendered row, the branch currents are 1 ampere and 1 ampere, adding back to 2 amperes. The output is above the threshold.

1\ \text{A}+1\ \text{A}=2\ \text{A},\quad 6\ \text{V}>5\ \text{V}

Loading can consume decision margin

The audit keeps the network and decision separate: first compute the loaded node, then compare it to the threshold. That order is why the final row changes state.

R_L\downarrow \Rightarrow V_o\downarrow,\quad \text{decision follows } V_o>V_{\text{threshold}}