Mixed Network Equivalent - Electricity and Electronic Circuits Step by Step

A mixed-network equivalent turns a series-plus-parallel layout into one resistance before using the source voltage to find total current. The staged reduction is exact only for the declared resistor values, ideal wires, ideal source, steady DC, and no self-heating; real circuits add resistor tolerance, lead and contact resistance, meter loading, supply variation, parasitics, temperature drift, and voltage/current measurement uncertainty.

A mixed circuit is reduced in stages: equal parallel branches first, then the remaining series resistance. 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 mixed circuit has one part before a split

Current first passes through the series resistor, then reaches a junction where it can split into two equal branch resistors.

\text{series part} + \text{parallel part}

Reduce the equal parallel pair

The two equal branch resistors share the same endpoints. For equal branches, the pair acts like half one branch resistance.

R_{\parallel} = \frac{R_{\text{branch}}}{2} = 2\ \text{ohm}

Scan three mixed networks

Keep the source at 12 volts. Each row reduces the equal parallel pair, adds the series resistor, then reads the total current.

\begin{array}{c|c|c|c|c}R_{\text{s}}&R_{\text{branch}}&R_{\parallel}&R_{\text{eq}}&I\\2\ \text{ohm}&4\ \text{ohm}&2\ \text{ohm}&4\ \text{ohm}&3\ \text{A}\\2\ \text{ohm}&2\ \text{ohm}&1\ \text{ohm}&3\ \text{ohm}&4\ \text{A}\\2\ \text{ohm}&8\ \text{ohm}&4\ \text{ohm}&6\ \text{ohm}&2\ \text{A}\\\end{array}

Add series resistance after reducing the split

For the shown circuit, the equivalent resistance is 4 ohm.

R_{\text{eq}} = 2\ \text{ohm} + 2\ \text{ohm} = \hl{4}\ \text{ohm}

Use the equivalent resistance for source current

The source current is 3 amperes. The equivalent one-resistor picture and the mixed topology therefore agree.

I = \frac{12\ \text{V}}{4\ \text{ohm}} = \hl{3}\ \text{A}

The voltage budget still closes

The series resistor drops 6 volts and the branch pair drops 6 volts. Those drops use the full source budget.

V_{\text{s}} + V_{\parallel} = 6\ \text{V} + 6\ \text{V} = \hl{12}\ \text{V}