Parallel Circuits
Components connected across the same two nodes
Theory
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What is a Parallel Circuit?
In a parallel circuit, components are connected across the same two nodes, creating multiple paths for current to flow. Each component has the same voltage across it, but the current divides among the branches.
Parallel Circuit Rules
- •Voltage is the same across all branches: V_total = V₁ = V₂ = V₃
- •Currents add up: I_total = I₁ + I₂ + I₃
- •Total resistance is LESS than the smallest individual resistance
- •If one branch fails, others continue to work (like modern house wiring)
Calculating Parallel Resistance
The total resistance of parallel resistors is found using the reciprocal formula. For two resistors, a simpler product-over-sum formula can be used: R_total = (R₁ × R₂) / (R₁ + R₂).
Real-World Parallel Circuits
Your home's wall outlets are all wired in parallel — each appliance gets the full mains voltage regardless of what else is plugged in. This is why turning off one lamp doesn't affect others. Car headlights, USB hubs, and server rack power distribution all use parallel wiring.
Kirchhoff's Current Law (KCL)
Kirchhoff's Current Law states that the total current entering a node equals the total current leaving it. In a parallel circuit, the current from the source splits at the first node, with each branch carrying a portion inversely proportional to its resistance. The branch with less resistance carries more current.
Formulas
Interactive Diagram
Interactive Circuit Diagram
Calculator
Enter any 2 values to calculate the rest
Circuit Challenges
Two resistors — 200Ω and 300Ω — are connected in parallel across a 12V source. Find the total resistance.
Calculate & fill in: