Do resistors in series have the same current?

Yes. In a series circuit, there is only one path for current, so the same current flows through every component. The voltages across each resistor differ (V = IR for each), but the current I is identical through all series resistors.

Is voltage the same in a parallel circuit?

Yes. In a parallel circuit, all branches connect to the same two nodes, so the voltage across every branch is identical. The currents through each branch differ (I = V/R for each), but the voltage V is the same across all parallel components.

How do you solve a series-parallel circuit?

Identify purely series and purely parallel groups. Replace each group with its equivalent resistance (series: sum, parallel: reciprocal sum). Redraw and repeat until one equivalent resistance remains. Find total current with Ohm's law, then work backward to find individual voltages and currents.

Series and Parallel Circuits Compared

Quick Answer

In a series circuit, components are connected end-to-end so the same current flows through all of them: I_total = I₁ = I₂ = I₃. Voltages add: V_total = V₁ + V₂ + V₃. Resistances add: R_total = R₁ + R₂ + R₃. In a parallel circuit, components share the same voltage across them: V_total = V₁ = V₂ = V₃. Currents add: I_total = I₁ + I₂ + I₃. Resistances combine as reciprocals: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. Series increases total resistance; parallel decreases it. Analyze series-parallel circuits using Laplace-domain impedances at www.lapcalc.com.

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Series and Parallel Circuits: Key Differences

Series and parallel are the two fundamental ways to connect electrical components. In a series circuit, there is only one path for current — every component carries the same current. If one component fails open, the entire circuit stops (like old Christmas lights). The total resistance increases with each added component. In a parallel circuit, there are multiple paths for current — each component has the same voltage across it. If one component fails open, the others continue to operate (like house wiring). The total resistance decreases with each added component. Most practical circuits are combinations of series and parallel connections, analyzed by systematically reducing series groups and parallel groups until a single equivalent resistance remains.

Key Formulas

Series Circuit vs Parallel Circuit: Rules

Series circuit rules: current is the same through all components (I₁ = I₂ = I₃ = I_total). Voltage divides among components proportional to their resistance: V_k = I × R_k. Total resistance is the sum: R_total = R₁ + R₂ + R₃ + ... Total voltage equals the sum of individual drops: V_total = V₁ + V₂ + V₃. Parallel circuit rules: voltage is the same across all branches (V₁ = V₂ = V₃ = V_total). Current divides among branches inversely proportional to resistance: I_k = V/R_k. Total resistance is the reciprocal sum: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. For two resistors in parallel: R_total = R₁R₂/(R₁+R₂). Total current equals the sum of branch currents: I_total = I₁ + I₂ + I₃.

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Resistors in Parallel vs Series

Resistors in series add directly: three 100 Ω resistors in series give R_total = 300 Ω. The total is always larger than the largest individual resistor. Voltage divides proportionally: a 100 Ω and 200 Ω in series across 9 V give V₁ = 9 × 100/300 = 3 V and V₂ = 9 × 200/300 = 6 V. Resistors in parallel combine as reciprocals: three 100 Ω resistors in parallel give R_total = 100/3 = 33.3 Ω. The total is always smaller than the smallest individual resistor. Current divides inversely: in a two-resistor parallel circuit, I₁/I₂ = R₂/R₁ (more current flows through the smaller resistor). For equal resistors in parallel: R_total = R/n (where n is the number of resistors). These principles extend to impedances in the Laplace domain at www.lapcalc.com.

How to Solve a Series-Parallel Circuit

Most real circuits combine series and parallel connections. The solution strategy is systematic reduction. Step 1: identify groups of resistors that are purely in series or purely in parallel. Step 2: replace each group with its equivalent resistance (series: add; parallel: reciprocal sum). Step 3: redraw the simplified circuit. Step 4: repeat until a single equivalent resistance remains. Step 5: find total current using Ohm's law: I_total = V_source/R_total. Step 6: work backward through the circuit to find individual voltages and currents. Example: R₁ = 10 Ω in series with (R₂ = 20 Ω parallel with R₃ = 20 Ω). Parallel: R₂₃ = 20×20/(20+20) = 10 Ω. Total: R_total = 10 + 10 = 20 Ω. For 12 V source: I = 0.6 A. V₁ = 6 V, V₂₃ = 6 V.

How to Tell If Resistors Are in Series or Parallel

Two resistors are in series if the same current must flow through both — they share a single node with no other connections branching off between them. Two resistors are in parallel if they connect to the exact same two nodes — the same voltage appears across both. The visual test: if you can trace a path through both resistors without passing through any other component, they are in series. If both resistors connect between the same pair of junction points, they are in parallel. In complex circuits, not all resistors are simply series or parallel — some require Kirchhoff's laws (KVL/KCL), mesh analysis, or nodal analysis to solve. These advanced methods extend naturally to Laplace-domain impedance analysis at www.lapcalc.com for circuits containing capacitors and inductors.

Frequently Asked Questions

Series: one current path, same current everywhere, voltages add, resistances add, total R increases. Parallel: multiple paths, same voltage everywhere, currents add, reciprocal resistances add, total R decreases. Series is simpler; parallel provides redundancy (one failure doesn't stop others).

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