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

A load on a divider output parallels the bottom resistor, so changing only the load moves the lower equivalent resistance, the source current, and the output node voltage. With fixed divider resistors the 6, 3, and 2 ohm loads give output voltages of 6, 24/5, and 4 V exactly for the ideal resistor model; real dividers add resistor tolerance, source impedance, loading, contact resistance, heating, supply limits, temperature drift, and voltage and current measurement uncertainty.

A load changes the lower equivalent resistance, source current, and output node voltage in exact rows. 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 load becomes part of the lower branch

The top and bottom divider resistors stay fixed. Only the load resistance changes, so the output voltage moves because the lower parallel branch changes.

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

Load resistance sets the output node

Read each row from load resistance to lower equivalent, source current, and output voltage. Smaller load resistance pulls the node lower.

\begin{array}{c|c|c|c}R_L&R_b\parallel R_L&I_s&V_o\\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}\\2\ \text{ohm}&\tfrac{3}{2}\ \text{ohm}&\tfrac{8}{3}\ \text{A}&4\ \text{V}\\\end{array}

The rendered row is the clean integer case

For the rendered row, the load is 6 ohm, the lower equivalent is 3 ohm, and the output node is 6 volts.

3\ \text{ohm}\cdot2\ \text{A}=6\ \text{V}