Parallel Circuits

Same Voltage in Parallel

shared endpoints

Parallel branches share the same two endpoints, so each branch gets the full source voltage.

Example

Parallel branches share the same two endpoints, so each branch gets the full source voltage. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Parallel branches share two buses

Both resistors connect from the same left bus to the same right bus. That shared connection is the structure that makes the branches parallel.

parallel⇒same two endpoints\text{parallel} \Rightarrow \text{same two endpoints}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA6 ohm3 ohm

Both branches share the same voltage row

A different battery could put a different voltage across the two buses, but within one parallel circuit both branches get that same bus-to-bus voltage. Each row is one possible source voltage.

VsourceVRaVRb6 V6 V6 V12 V12 V12 V18 V18 V18 V\begin{array}{c|c|c}V_{\text{source}} & V_{\text{Ra}} & V_{\text{Rb}} \\6\ \text{V} & 6\ \text{V} & 6\ \text{V} \\12\ \text{V} & 12\ \text{V} & 12\ \text{V} \\18\ \text{V} & 18\ \text{V} & 18\ \text{V}\end{array}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA6 ohm3 ohm+-12 V+-12 V

Each branch gets the source voltage

Since each branch is connected across the same two battery endpoints, each branch gets the full 12 volts.

VRa=VRb=12 VV_{\text{Ra}} = V_{\text{Rb}} = \hl{12}\ \text{V}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA6 ohm3 ohm+-12 V+-12 V
electricity A parallel circuit is defined by topology: distinct branches connect across the same two buses.