Mixed Network Equivalent - Electricity & Circuits Step by Step

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}