Parallel Equivalent Resistance - Electricity and Electronic Circuits Step by Step

A parallel network's equivalent resistance is the source voltage divided by the total current drawn from the source.

electricity The two-branch network draws 6 A from a 12 V source, so it acts like one 2 ohm equivalent resistance.

Example

A parallel network's equivalent resistance is the source voltage divided by the total current drawn from the source. 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 source only sees the total current

From the battery's point of view, the two branches together draw 6 amperes.

I_{\text{total}} = 6\ \text{A}

More total current means lower equivalent resistance

Keep the source at 12 volts and compare possible total currents. If the network draws more current from the same voltage, the equivalent resistance is smaller.

\begin{array}{c|c|c}V & I_{\text{total}} & R_{\text{eq}} \\12\ \text{V} & 3\ \text{A} & 4\ \text{ohm} \\12\ \text{V} & 6\ \text{A} & 2\ \text{ohm} \\12\ \text{V} & 12\ \text{A} & 1\ \text{ohm}\end{array}

Use total current to find equivalent resistance

The equivalent resistance is the source voltage divided by the total current. Here the two-branch network acts like one 2 ohm resistor.

R_{\text{eq}} = \frac{V}{I_{\text{total}}} = \frac{12\ \text{V}}{6\ \text{A}} = \hl{2}\ \text{ohm}