Series and parallel circuits come down to two sentences, and the Texas exam tests what follows from them

What the exam asks about it

Thirty-nine of the five hundred questions in our bank sit in the theory area, and series and parallel arrangements are the outright subject of eight of them. Two ask which quantity is shared. Four ask for a combined resistance. One asks whether a parallel result lands above or below the branch values, with no arithmetic needed to answer it. One works a series-parallel network end to end and asks for the current in a single branch.

Those eight are the visible share. The arrangement decides the answer inside a great many more, because loads on a branch circuit are in parallel, control devices are in series, and a conductor's own resistance sits in series with whatever it feeds.

On the Texas papers, PSI gives the subject line Definitions, Theory, and Plans 3 of the 56 scored items on the journeyman knowledge portion, and Calculations and Theory 2 of the 24 on the calculations portion, in the candidate information bulletin for the TDLR electricians program updated 9 July 2026. Master candidates get 7 of 70 and 2 of 30.

The two sentences the topic reduces to

In a series circuit the same current flows through every element, and the voltages across them add up to the source voltage.

In a parallel circuit the same voltage sits across every element, and the currents through them add up to the total.

That is the whole topic. Every formula you've seen for combining resistances is a consequence of one of those two sentences. Series resistances add, because the current is common and the voltages stack. Parallel conductances add, because the voltage is common and the currents stack, and resistance is the reciprocal of conductance.

Say the arrangement out loud as a pair before you touch a formula: what's shared, and what divides. Series shares current and divides voltage. Parallel shares voltage and divides current. The worked derivations and the long-hand reciprocal arithmetic live in the series parallel question set. This page is about how Texas tests it.

Which quantity splits, and in which direction

How the split happens is worth one line each, because items get written on it. Voltage divides in proportion to resistance, so the largest element in a series string takes the largest share. Current divides inversely with resistance, so the smallest branch in a parallel set takes the largest share. People learn one of those and apply it to both.

The bank's series-parallel network question is built on exactly that. A 10 ohm resistor sits in series with a parallel pair of 30 and 60 ohms, all across 120 volts. The pair combines to 20 ohms, the total is 30 ohms, and the source delivers 4 amperes. All 4 amperes cross the 10 ohm resistor and drop 40 volts, leaving 80 volts across the parallel section, so the 30 ohm branch carries 2.67 amperes while the 60 ohm branch carries 1.33. The two branch currents add back to 4, which is your check.

Every wrong option on that item is a real quantity from somewhere in the circuit, including the total current and the current in the other branch. That is the shape of a well-written distractor, and it's worth recognizing. The options are rarely random numbers. They are answers to questions you were asked to ignore.

The check that catches your own errors

A total parallel resistance always lands below the smallest branch. Always, with no exception anywhere. The 20 ohms above sits under the 30 ohm branch, so it passes. Where a parallel answer comes out above one of the branches there's an arithmetic error in it, and you've caught it in two seconds without rechecking a single step of your work.

The series check runs the other way: the total always lands above the largest element.

The bank has a question that asks for nothing else. Two resistances of 8 and 24 ohms in parallel, and the four options are above 24, between 8 and 24, below 8, and exactly 16. The answer is below 8, and the whole item is answerable before you calculate anything. The option at exactly 16 is the average of the two, which is how a candidate reaching for a half-remembered formula arrives at a number the check throws straight out.

Run the check on every answer, including the ones a shortcut gave you. That is the habit that makes a shortcut safe to use under a clock, because a shortcut used outside its conditions produces a number the check refuses.

Two shortcuts and the condition on each

Two shortcuts answer most parallel items with no fractions at all, and each one carries a condition you have to learn alongside it.

Equal branches: divide by how many there are

Three equal branches of 12 ohms give 4 ohms. Two equal branches of 15 ohms give 7.5 ohms. The rule is the branch value divided by the number of branches, and it holds while the branches are equal to each other. Two identical heaters on the same two wires give you half the branch value before you've finished reading the sentence.

Exactly two branches: product over sum

For two branches and only two, multiply them together and divide by their sum. Thirty and sixty ohms give 1,800 over 90, which is 20 ohms. The word exactly is the condition. Applied to a three-branch set it returns a figure larger than every branch in the circuit, which the sanity check throws out immediately.

Averaging the branches is the repair people reach for when the branches are unequal, and it produces a number above the smallest branch every time, so the check catches that one too. Where you have three or more unequal branches, either work two at a time and combine the result with the third, or go to reciprocals.

Where this decides a code answer

Four places where the arrangement settles an item that carries a code label.

• Branch circuit loads. Every receptacle and every luminaire on a circuit sits across the same two conductors, so the circuit current is the sum of the branch currents. A load calculation is a very long parallel circuit problem wearing a code book.
• Control strings. A contactor coil with a stop button, a float switch and an overload contact ahead of it is a series string, and every device has to be closed for the coil to pull in. That is the troubleshooting shape as well, since one open kills a series string while one dead load on a parallel arrangement points straight at that load.
• Paralleled conductors. Run two conductors as one and the current divides by impedance, so a set whose paths differ loads one conductor harder than its partner while the device ahead of them sees only the total. NEC 310.10(G) answers that with conditions about the conductors matching each other.
• Devices in parallel. NEC 240.8 permits fuses and circuit breakers in parallel only where they were factory assembled in parallel and listed as a unit. Two devices joined at both ends share current in inverse proportion to impedance, exactly as two conductors do.

Our page on multiwire branch circuits is where these two arrangements collide hardest, because a lost neutral turns two parallel loads into one series pair across 240 volts.

The open element, and what it costs

Three heating elements in series across 240 volts, and one of them burns open. What stands across the break is the full 240 volts.

That answer catches people because it feels backward. With the string open no current flows anywhere in it, and voltage drop is current times resistance, so the two intact elements drop nothing at all. The element that has stopped conducting is the one holding the whole supply. The bank offers 80 volts as the element's equal share, for anybody who kept the current flowing in their head, and zero volts for anybody who read no current as meaning no voltage.

On the job that's a live hazard sitting inside equipment that looks dead, which is the practical reason the topic is examinable. It's also the fastest way to find the failed element: read across each one in turn, and the one showing supply voltage is the open.

The same two arrangements decide how much power a fixed pair of elements draws. Two 30 ohm elements across 240 volts draw 3,840 watts wired in parallel and 960 watts wired in series, because the parallel pair is 15 ohms and the series pair is 60. Nothing about the elements changed. The connection did, and the power fell to a quarter. Both figures come out of voltage squared divided by resistance, which is one of the four rearrangements set out on our page about Ohm's law and the exam arithmetic.

What to do about it before test day

Three drills and one habit.

1. Name the arrangement out loud before you write anything down. Shared current means series. Shared voltage means parallel.
2. Do twenty parallel combinations from memory, alternating equal branches with unequal pairs, until both shortcuts and their conditions come without thinking.
3. Work one series-parallel network a day from the inside out. Combine the parallel section, add the series element, find the total current, then walk the voltage back down to the branch you were asked about.

The habit is the sanity check, run on every answer including the ones you feel sure of. It costs two seconds and it's the only error trap on the paper that works without rechecking your arithmetic.

Texas runs the exam open book, and none of this sits in the book. The calculations portion allows 110 minutes for 26 items, so the seconds you save here are seconds the code lookups get. That trade is the whole argument for drilling theory at all, given that theory itself is five scored items out of eighty. TDLR passed 20.6 percent of the 6,328 candidates who sat the journeyman calculations portion in fiscal 2025, and time is most of what separates the two groups.

Questions people ask

What is the difference between a series and a parallel circuit?

Series shares current and parallel shares voltage. In a series circuit there's one path, so the same current flows through every element and the voltages across them add up to the source. In a parallel circuit every branch connects the same two points, so every branch sees the same voltage and the branch currents add up to the total. Everything else follows from those two facts. Series resistances add, parallel conductances add, and a parallel total always lands below its smallest branch while a series total lands above its largest element.

How do you find the total resistance of resistors in parallel?

Add the reciprocals and invert the result. Two shortcuts save you the fractions where their conditions hold. Where the branches are equal to each other, divide the branch value by the number of branches, so three 12 ohm branches give 4 ohms. Where there are exactly two branches of any values at all, multiply them and divide by their sum, so 30 and 60 give 1,800 over 90, which is 20 ohms. Then check whichever route you took against the branch values, because a parallel total above the smallest branch has an error in it.

How many series and parallel questions are on the Texas exam?

Theory carries five scored items across the two journeyman papers, and series and parallel arrangements sit inside that line as part of it. PSI's content outline gives Definitions, Theory, and Plans 3 of the 56 scored items on the knowledge portion and Calculations and Theory 2 of the 24 on the calculations portion. Master candidates get 7 of 70 and 2 of 30. The arrangement decides the answer inside many more items than that, because branch circuit loads are parallel and conductor resistance sits in series with the load it feeds.

What happens when one element in a series string opens?

Everything in the string stops, and the full supply voltage stands across the break. No current flows, and voltage drop is current times resistance, so the intact elements drop nothing at all while the open one holds the whole supply. That makes it a live hazard inside equipment that looks dead. It's also the quickest diagnosis available to you: read voltage across each element in turn, and the one showing supply voltage is the failed one. A parallel arrangement behaves the opposite way, where one open branch stops and the others carry on.

Why does the code put conditions on paralleled conductors?

Because the current divides by impedance. Two conductors joined at both ends share the load in inverse proportion to their impedance, so a set whose paths differ in length, material or termination loads one conductor harder than its partner, while the overcurrent device ahead of them reads only the total and stays closed through it. NEC 310.10(G) answers that with conditions about the conductors matching each other. NEC 240.8 takes the same physics to overcurrent devices and permits them in parallel only where a manufacturer assembled and listed the pair as one unit.

Is a load calculation really a parallel circuit problem?

In its arithmetic, yes. Every receptacle, luminaire and appliance on a circuit sits across the same two conductors, which is what a parallel arrangement means, and the circuit current is the sum of the individual branch currents. That summing is what a load calculation does, with code rules deciding which loads count at full value and which get a demand factor applied. Knowing the arrangement will tell you why the numbers add the way they do, and the book is still where you find which factor applies to what.