Parallel Circuits

Open Branch Contrast

one branch can fail alone

Opening one parallel branch does not break the other branch; the remaining branch still has the source voltage across it.

Example

Opening one parallel branch does not break the other branch; the remaining branch still has the source voltage across it. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One branch can open

Opening the switch breaks the upper branch. The lower branch is still connected across the battery buses.

upper branch open, lower branch still connected\text{upper branch open, lower branch still connected}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA4 Aopen6 ohm3 ohm4 A4 A

Opening one branch removes only that branch current

After the upper branch opens, its current is zero. The remaining branch still sets the source total, so the total equals whatever current the lower branch carries.

IRaIRbItotal0 A2 A2 A0 A4 A4 A0 A6 A6 A\begin{array}{c|c|c}I_{\text{Ra}} & I_{\text{Rb}} & I_{\text{total}} \\0\ \text{A} & 2\ \text{A} & 2\ \text{A} \\0\ \text{A} & 4\ \text{A} & 4\ \text{A} \\0\ \text{A} & 6\ \text{A} & 6\ \text{A}\end{array}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA4 Aopen6 ohm3 ohm4 A4 A

The other branch keeps its current

The lower branch still has the same 12 volts across the same resistor, so it still carries 4 amperes.

IRb=12 V3 ohm=4 AI_{\text{Rb}} = \frac{12\ \text{V}}{3\ \text{ohm}} = \hl{4}\ \text{A}
Parallel branches share the same busesA battery feeds two distinct resistor branches connected between the same left and right buses.12 VA4 Aopen6 ohm3 ohm4 A4 A
electricity When one branch opens, the other branch remains connected across the same battery buses and keeps carrying its own current.