Definition

A parallel circuit gives current more than one path to follow, each bulb or device sits on its own branch, so if one stops working the others keep going, and adding more bulbs does not make the others dimmer, since each branch gets the full push from the source. Components are connected across the same two points, forming separate branches; every branch receives the full source voltage, current splits among the branches with more current taking lower-resistance paths, total current equals the sum of the branch currents, and combined resistance is less than any single branch: $1/R_{\text{total}} = 1/R_1 + 1/R_2 + \ldots$. The loop rule forces equal voltage across every branch and the junction rule gives $I_{\text{total}} = \sum V/R_i$, so $1/R_{\text{eq}} = \sum 1/R_i$, for two resistors $R_{\text{eq}} = R_1R_2/(R_1 + R_2)$; current divides inversely with resistance by the current-divider rule, power in each branch is $V^2/R_k$ so the smallest resistance dissipates the most, parallel capacitors add directly, and household wiring is parallel at a fixed $120\ \text{V}$ so every appliance operates independently at that rated voltage.