Parallel Circuits

Parallel Equivalent Resistance

total current decides

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

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.

Itotal=6 AI_{\text{total}} = 6\ \text{A}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA6 A6 ohm3 ohm6 A2 A4 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.

VItotalReq12 V3 A4 ohm12 V6 A2 ohm12 V12 A1 ohm\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}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA6 A6 ohm3 ohm6 A2 A4 A

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.

Req=VItotal=12 V6 A=2 ohmR_{\text{eq}} = \frac{V}{I_{\text{total}}} = \frac{12\ \text{V}}{6\ \text{A}} = \hl{2}\ \text{ohm}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA6 A6 ohm3 ohm6 A2 A4 A
electricity The two-branch network draws 6 A from a 12 V source, so it acts like one 2 ohm equivalent resistance.