What are Series and Parallel Circuits?
In a series circuit, components are connected end-to-end so the same current flows through each one. In a parallel circuit, components share the same voltage across separate branches, so current splits between them.
In series, resistances add directly (R = R1+R2+…); in parallel, their reciprocals add (1/R = 1/R1+1/R2+…), which always lowers the total resistance below the smallest branch.
- •Single path for current
- •Same current through all parts
- •Resistances add: R = R1+R2+…
- •One broken component stops the whole circuit
- •Voltage divides across components
- •Multiple paths (branches) for current
- •Same voltage across all branches
- •1/R = 1/R1+1/R2+…
- •One broken branch doesn't stop the others
- •Current divides across branches
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Step-by-step worked examples
Two resistors, 4 Ω and 6 Ω, are connected in series. Find the total resistance.
R = R1 + R2 R = 4 + 6 R = 10 Ω
The same two resistors, 4 Ω and 6 Ω, are connected in parallel instead. Find the total resistance.
1/R = 1/R1 + 1/R2 1/R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 R = 12/5 = 2.4 Ω
Three identical 2 Ω bulbs are wired in series across a 12 V battery. Find the current.
R_total = 2+2+2 = 6 Ω I = V/R = 12/6 I = 2 A
Flashcards
Quick quiz
Q1.Two 5 Ω resistors are connected in series. What is the total resistance?
Q2.Two 5 Ω resistors are connected in parallel. What is the total resistance?
Q3.In a series circuit, what stays the same through every component?
Q4.Why do household outlets use parallel wiring instead of series?
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Common mistakes
Adding resistances directly in a parallel circuit. — Correct: Add reciprocals instead: 1/R = 1/R1+1/R2+…
Assuming voltage is the same in a series circuit. — Correct: In series it's current that stays the same; voltage divides across components.
Assuming current is the same in a parallel circuit. — Correct: In parallel it's voltage that stays the same; current divides across branches.
Thinking one broken component always stops a circuit. — Correct: Only true in series. In parallel, other branches keep working.
FAQ
What is the difference between series and parallel circuits?
In series, components share one path and the same current; in parallel, components share the same voltage across separate branches.
What is the formula for series and parallel circuits?
Series: R = R1+R2+…. Parallel: 1/R = 1/R1+1/R2+…
What are examples of series and parallel circuits?
Old-style Christmas lights are often series; household wiring and most electronics use parallel circuits.
How do you calculate total resistance in series and parallel circuits?
Add resistances directly for series, or add their reciprocals and invert the result for parallel.