Parallel Circuits — Voltage, Current, Impedance & Voltage Drop Reference
Parallel circuit reference for the engineering meaning: voltage in series and parallel formula, parallel voltage and parallel current laws, parallel impedance calculator workflow, and the parallel circuit voltage drop calculator that sizes the feeder to a multi-branch load. Includes the parallel axis theorem (mechanics) and disambiguation of geographic latitude parallels (32nd, 38th, 40th, and the film "Parallel 2018"). Reviewed by a licensed PE.
Parallel circuit voltage drop calculator
This embedded voltage drop calculator (also acts as a parallel calculator, parallel line calculator, parallel impedance calculator, and voltage drop parallel circuit calculator) sizes the conductor feeding any parallel-branch load. Enter total branch current, voltage, and run length; it returns voltage drop, % drop, and NEC compliance pass/fail.
- Drop ratio
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- V at load
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- Power loss
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- ρ used (T-corrected)
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Parallel circuit formulas
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- Series — voltages add to the source voltage (Kirchhoff's voltage law)
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- Parallel — every branch sees the same source voltage
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- Hybrid networks combine the two rules region-by-region
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- Each branch current is V / R_i (Ohm's Law per branch)
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- Total current at the supply equals the sum (Kirchhoff's current law)
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- Conductor feeding the parallel section must carry I_total
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- For two branches, the product-over-sum shortcut applies
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- For AC, replace R with complex Z = R + jX
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- R_eq is always less than the smallest individual branch
Standards and authoritative references
| Standard / source | Relevance |
|---|---|
| NEC 310.10(H) | Standard practice for paralleling conductors — minimum size #1/0 AWG, identical length / material per phase |
| NEC 240.21 | Tap rules for parallel feeders and branches |
| IEEE Std 100 | Authoritative dictionary of IEEE terms — definitions of series, parallel, and hybrid networks |
| IEC 60050-131 | International electrotechnical vocabulary — circuit theory terminology |
| NIST SP 811 | SI units used in voltage and current measurement |
Reference: parallel circuit examples and worked currents
| Source | Branches | Branch currents | Total / R_eq |
|---|---|---|---|
| 120 V residential branch | 10 outlets, each with a 100 W LED lamp | 0.83 A each | I_tot = 8.33 A; R_eq = 14.4 Ω |
| 240 V dryer branch | 5 kW heater + 0.5 kW motor | 20.83 A + 2.08 A | I_tot = 22.9 A; R_eq = 10.5 Ω |
| 12 V automotive bus | Headlight (4.6 Ω) || radio (24 Ω) || ECU (60 Ω) | 2.61 A + 0.5 A + 0.2 A | I_tot = 3.31 A; R_eq = 3.62 Ω |
| 480 V 3-φ feeder, paralleled #4/0 Cu | 2 sets of #4/0 (NEC 310.10(H)) | 200 A each | I_tot = 400 A; effective Z halved |
- Identify the branches and the source. A parallel circuit has two or more branches connected to the same pair of nodes. The source supplies one voltage to all branches simultaneously; each branch carries its own current set by its own impedance.
- Apply the parallel-circuit voltage rule. Voltage across every parallel branch is the same and equal to the source voltage (no Kirchhoff voltage drop accumulates as you walk between branches in parallel). This is why every receptacle in a residential wiring branch sees the same nominal mains voltage.
- Compute branch currents from Ohm's Law per branch. I_i = V / R_i for each branch i. The current divides between branches in inverse proportion to their resistance: a 100 Ω branch sees 10× the current of a 1 000 Ω branch from the same source.
- Compute total current as the sum of branch currents. I_total = I_1 + I_2 + … + I_n (Kirchhoff's current law, KCL — sum of currents into any node equals zero). The conductor feeding the parallel section must carry I_total, so size it accordingly.
- Compute equivalent parallel resistance / impedance. R_eq = 1 / (1/R_1 + 1/R_2 + … + 1/R_n). Two branches: R_eq = R_1 · R_2 / (R_1 + R_2). For complex impedance: 1/Z_eq = 1/Z_1 + 1/Z_2 + …, with Z values complex (R + jX). The equivalent is always smaller than the smallest individual branch.
Worked example — three loads in parallel on a 240 V branch
A 240 V single-phase branch feeds three parallel loads through 30 m of #10 AWG copper: a 5 kW resistive heater, a 1 kW motor (PF 0.85), and a 200 W LED panel array (PF 1.0). Find branch currents, total current, equivalent impedance, and voltage drop on the feeder.
Step 1 — branch currents: heater I_1 = 5000 / 240 = 20.83 A; motor I_2 = 1000 / (240 × 0.85) = 4.90 A; LED I_3 = 200 / 240 = 0.83 A.
Step 2 — total current: I_total = 20.83 + 4.90 + 0.83 = 26.56 A.
Step 3 — equivalent resistance (resistive equivalent): R_eq = V / I_tot = 240 / 26.56 = 9.04 Ω.
Step 4 — voltage drop on the feeder: V_drop = 2 × 30 × 26.56 × 0.0175 / 5.26 = 5.30 V (= 2.21 % of 240 V — within the 3 % branch limit per NEC 210.19(A)).
Step 5 — voltage at the loads: V_loads = 240 − 5.30 = 234.70 V. All three loads see this same reduced voltage, so the heater delivers 4.78 kW (vs. 5.0 kW nominal — a 4.4 % power reduction from the conductor drop).
Series vs parallel — when each one is used
| Property | Series circuit | Parallel circuit |
|---|---|---|
| Voltage | Divides among elements (V_1 + V_2 + … = V_src) | Same across every branch (V_branch = V_src) |
| Current | Same through every element (I_1 = I_2 = …) | Divides among branches (I_1 + I_2 + … = I_total) |
| Equivalent resistance | R_eq = R_1 + R_2 + … (always larger than any single R) | 1/R_eq = Σ(1/R_i) (always smaller than any single R) |
| If one element fails open | Whole circuit stops working (Christmas tree lights) | Other branches keep working (residential outlets) |
| If one element shorts | Other elements may overcurrent / fail | Source may overcurrent; branch fuse trips |
| Common use | String of LEDs sharing current; voltage divider; over-current sensing shunt | Residential / commercial wiring; appliance buses; battery cells in parallel for capacity |
Variants and disambiguation
Parallel circuit — the engineering meaning
The dominant engineering meaning of "parallel circuit" — the wire in parallel and parallel wiring of every household receptacle, every appliance branch, every battery-cell bank in parallel for added capacity. The voltage source in parallel arrangement (e.g., two paralleled 12 V batteries) increases capacity at the same voltage. Used universally because failure of one branch does not bring down the others, unlike a series chain.
Parallel cord — extension cords with multiple outlets
A parallel cord (also called a multi-outlet cord, gang cord, or power strip) is a single inlet plug feeding several parallel-wired outlets. NEC 400 governs the cord specification; UL 817 lists relocatable power-tap requirements. The supply current must not exceed the cord rating (typically 13 A for 16 AWG, 15 A for 14 AWG).
Parallel power — paralleling sources for higher capacity
Parallel power describes paralleling generators, batteries, or PV inverters to share load. Paralleling generators requires synchronisation (matching voltage, frequency, and phase before closing the breaker). Paralleling batteries requires equal cell voltages before connection to avoid huge equalisation currents. Paralleling PV inverters needs each inverter\'s anti-island scheme to recognise the others.
Geographic parallels — disambiguation
Outside circuit analysis, "parallel" most often means a line of latitude. The 32nd parallel north (Texas, North Africa), 38th parallel north (Korea border), 40th parallel north (Beijing, Philadelphia, Madrid), and the "parallel 40" are the most-searched. None bear on electrical engineering — included here for query disambiguation.
Frequently asked questions
- How to calculate parallel circuits?
- How to calculate parallel circuits — apply three rules: (1) voltage across every parallel branch equals the source voltage; (2) current in each branch is V / R_i (Ohm's Law per branch); (3) total current is the sum of branch currents, and equivalent resistance is the inverse of the sum of inverses, R_eq = 1 / Σ(1 / R_i). For two branches the shortcut is R_eq = R_1 · R_2 / (R_1 + R_2).
- How to find voltage drop in parallel circuit?
- How to find voltage drop in parallel circuit: voltage across each branch is identical to the source voltage — there is no incremental drop walking between parallel branches. The voltage drop only appears across the wire feeding the parallel section: V_drop = I_total × R_wire. For a real installation, use the voltage drop calculator below with I = total branch current.
- What is parallel voltage?
- Parallel voltage is the voltage that appears across every branch of a parallel network. Because all branches share the same two nodes, they all see the same potential difference. This is the defining property of a parallel circuit, contrasted with a series circuit where the source voltage divides among the elements.
- What is parallel circuit voltage drop?
- Parallel circuit voltage drop is conventionally measured on the conductor feeding the parallel section, not across any single branch (which sees the full source voltage). Use V_drop = I_total × (2·L·ρ/A) for the round-trip drop, where I_total is the sum of all branch currents. The parallel circuit voltage drop calculator below applies this directly.
- What is the standard parallel?
- In geography, a "standard parallel" is a line of latitude used as a reference in cartographic projections — the Lambert conformal conic projection uses one or two standard parallels to minimise distortion across the mapped area. In electrical engineering, "standard parallel" usually refers to the standard practice of paralleling identical components (e.g., paralleling two #4 AWG conductors per NEC 310.10(H) for a 200 A feeder).
- What is parallel vs vertical?
- Parallel vs vertical describes two ways of arranging an installation. Parallel: components or runs lie alongside one another, sharing endpoints. Vertical: components run perpendicular to the parallel direction (top-down). For wire-tray and cable-management work, parallel runs share fill-percentage limits per NEC 392; vertical drops follow separate support-spacing rules.
- What is the parallel axis theorem?
- The parallel axis theorem (used by the parallel axis theorem calculator) is from mechanics, not circuits: I = I_centroid + A · d², giving the moment of inertia of an area about an axis parallel to and offset by distance d from a centroidal axis. Used in beam-section moment-of-inertia composites — see the dedicated composite-centroid calculator.
- What does "parallel 2018", "parallel 40", "32nd parallel" refer to?
- Geographic latitude lines (terms unrelated to electrical parallel circuits but cluster together in search). The 32nd parallel north passes through northern Africa, Israel, southern US (San Antonio, Phoenix). The 38th parallel north is famous as the Korea border. The 40th parallel north passes through Madrid, Beijing, Philadelphia. "Parallel 2018" is the title of a 2018 South Korean film. None bear on circuit analysis — included here only for query disambiguation.
Kirchhoff\'s 1845 statement of the parallel-circuit law
The sum of the currents flowing into any node of a network of conductors is equal to the sum of the currents flowing out of the same node. The sum of the electromotive forces around any closed loop is equal to the sum of the products of resistance and current around that loop. Together these two laws fully determine the currents and voltages in any network of branches, regardless of the topology — series, parallel, or any combination thereof.
Related calculators and references
Sources and further reading
- Kirchhoff, G. R. Ueber den Durchgang eines elektrischen Stromes durch eine Ebene. Annalen der Physik, 1845. Original statement of the circuit laws.
- Hayt, W. H.; Kemmerly, J. E.; Durbin, S. M. Engineering Circuit Analysis, 9th ed. McGraw-Hill, 2018. Standard undergraduate text on series and parallel networks.
- NFPA. NFPA 70 — National Electrical Code (2023). Articles 210, 240, 310.10(H), and 392 — branch wiring and paralleled conductors.
- IEEE. IEEE Std 100 — The Authoritative Dictionary of IEEE Standards Terms, 7th edition.
- IEC. IEC 60050-131 — International Electrotechnical Vocabulary, Part 131: Circuit theory.
- Mike Holt Enterprises. Understanding the National Electrical Code, Vol. 1. Standard reference for paralleled-conductor practice.