Short answer: In a series circuit there is one path, so the same current flows through every part, the resistances add up and the voltage splits between them. In a parallel circuit every branch gets the full voltage, the branch currents add up, and the total resistance is lower than the smallest branch. Receptacles and lighting loads are generally connected in parallel across their supply conductors, so each receives the circuit’s nominal voltage. Individual switches can still be connected in series with their controlled loads. For a normal sinusoidal AC supply, 120 or 240 volts refers to the RMS voltage. US utility power operates at 60 Hz, or 60 complete cycles per second.
Tsai Electro is an independent learning site. Not affiliated with TDLR, PSI or NFPA.
Total resistance, series and parallel
Series and parallel resistance calculator
Enter up to four resistances in ohms and a supply voltage. This calculator models ideal resistors only. It does not calculate impedance, reactance or power factor for AC motors and other reactive loads. Leave a box at 0 to skip it: 0 here means no resistor in that spot, not a zero-ohm short. The starting example is two 12-ohm loads on 120 volts.
- Resistance 1, ohms
- Resistance 2, ohms
- Resistance 3, ohms
- Resistance 4, ohms
- Supply voltage, volts
Series and parallel side by side
| Series | Parallel | |
|---|---|---|
| Paths for current | One | One per branch |
| Current | Same through every part | Splits; branch currents add up to the total |
| Voltage | Splits; the drops add up to the supply | Full supply voltage across every branch |
| Total resistance | Sum of all resistances | Less than the smallest branch |
| If one part opens | Everything stops | The other branches keep working |
| Where you see it | A switch in series with its light, a fuse in series with its load | Receptacles and lights on a branch circuit |
Two quick rules for parallel: two equal resistances in parallel are half of one, and the formula for any number is 1 / (1/R1 + 1/R2 + …). In this simple resistive model, that is also why adding more loads in parallel raises the current: each new branch lowers the total resistance. Real AC loads such as motors also have reactance, so the numbers are not this simple.
AC basics in plain words
- Alternating current reverses direction many times a second. In the United States the standard frequency is 60 hertz, 60 full cycles per second.
- RMS and peak. A true-RMS meter reads the RMS (effective) value; many basic meters are accurate only on a clean sine wave. For a clean sine wave the peak is about 1.414 times the RMS, so a 120-volt circuit peaks near 170 volts.
- Single phase and three phase. Homes usually get 120/240-volt single phase. Many commercial buildings get three phase, such as 208Y/120 or 480Y/277 volts.
- Power factor. Motors and other inductive loads make the current lag the voltage. For single-phase AC, real power in watts equals RMS volts x RMS amps x power factor, so below a power factor of 1 it is less than volts x amps.
- Three-phase power for a balanced load is line-to-line volts x line amps x 1.732 x power factor.
Ohm’s law still works for resistive AC loads like heaters. Coils and capacitors add reactance, which is why motor and transformer math has its own formulas.
Starting your first year as a Texas apprentice? The US$19 Texas First-Year Electrical Apprentice Kit gives you printable pages for the first months on the job: a tool-check card, a who-to-ask list with a short stop-and-ask script, emergency-contact and heat-and-rest cards, plus a Tool budget sheet and a Tool inventory sheet (CSV).
Log your Texas Journeyman hours free. A free Tsai Electro account keeps your supervised hours, your online practice scores and your exam date in one place. Start with a five-question check to see which topic to practice next.
The free hours ledger in your Tsai Electro account lets you record each employer, supervisor, work period and hours, shows how far you are from 7,000, 8,000 and 12,000 hours, and exports a CSV or a printable summary. It is your own record, not an official TDLR record, and it does not replace the Experience Verification Form your supervising Master signs.
As an Amazon Associate, Tsai Electro earns from qualifying purchases. Prices and stock change on Amazon, so check the listing before you buy.
Ugly’s Electrical References, 2026 Edition
A pocket book with the series, parallel, single-phase and three-phase formulas in one place, useful while you practice these calculations.
The Journeyman exam tests electrical theory. The PSI bulletin lists Electrical Theory in both the NEC Knowledge portion and the Calculations portion of the Texas Journeyman exam. The Texas Journeyman Electrician Exam Practice Pack has 1,000 original practice questions in the PSI two-part format, 10 full timed two-part mocks and step-by-step solutions for every calculation question, built on the 2026 NEC. It is exam prep only, not a theory course. One payment of US$39, no subscription, and you can try 70 questions free with no sign-up.
Are house outlets wired in series or parallel?
In parallel. Each receptacle and light on a branch circuit gets the full circuit voltage, and one device failing does not stop the others, as long as the shared wiring and connections ahead of it are intact.
Why is parallel resistance lower than the smallest resistor?
Every branch adds another path for current. More paths let more total current flow at the same voltage, and by Ohm’s law more current at the same voltage means lower total resistance.
Why does a 120-volt circuit peak at about 170 volts?
120 volts is the RMS value, the one a true-RMS meter shows and the one that does the same work as 120 volts DC. For a sine wave the peak is about 1.414 times the RMS, which is about 170 volts.
Sources checked October 2026
- PSI Candidate Information Bulletin 1682, Texas electrician exams (PDF, updated 9/15/2026)
- OSHA, 29 CFR 1910.399 definitions, nominal voltage examples such as 120/240 and 480Y/277 volts
- Series and parallel rules, RMS and power factor are standard physics and need no outside source.
