Practice: series and parallel circuits
Each problem uses new numbers, so you practice the method rather than memorizing an answer.
Pick the answer: sizes and ratings come from your code book.
Worked solution
Formula
| Symbol | Meaning | Unit |
|---|---|---|
| RT | Total (equivalent) resistance | Ω |
| R1, R2, R3 | Individual resistances | Ω |
| E | Source voltage, or the voltage across one part | V |
| I | Current | A |
Worked example
Three resistors of 31 Ω (R1), 33 Ω (R2) and 37 Ω (R3) are connected in series across a 24 V source. What is the voltage across R2?
- Series resistances add: RT = 31 + 33 + 37 = 101 Ω.
- The same current flows through every part of a series circuit: I = E ÷ RT = 24 ÷ 101 = 0.2376 A.
- Voltage across R2: E2 = I × R2 = 0.2376 × 33 = 7.84 V.
Answer: 7.84 V
Series and parallel circuits, explained
A series circuit has one path. The resistances add, the same current flows through every part, and the source voltage divides among the parts in proportion to their resistance. The voltage drops always add up to the source voltage.
A parallel circuit has several branches connected across the same two points, so every branch gets the full source voltage. The branch currents add up to the total current. Each added branch is another path for current, so the total resistance goes down and is always less than the smallest branch. For two resistors, use product over sum; for equal resistors, divide one value by how many there are.
A combination circuit has both. Reduce each parallel group to one equivalent resistance, add it to the series parts, and then work back out to find the current and voltage in each part. In the field, receptacles and lights on a branch circuit are parallel loads, and the circuit conductors are in series with them, which is why long runs cause voltage drop.
How to solve it on the exam
- Sketch the circuit and mark which resistors share one path (series) and which connect across the same two points (parallel).
- Reduce each parallel group to one equivalent resistance: product over sum for two, reciprocals for three or more, R ÷ n for n equal resistors.
- Add the series resistances, including any parallel equivalents, to get RT.
- Find the total current with I = E ÷ RT.
- Work back out: in series parts the current is the same and E = I × R; across parallel parts the voltage is the same and each branch current is E ÷ R.
Common mistakes
- Adding parallel resistances as if they were in series.
- Using product over sum on three resistors at once. It works only two at a time.
- Forgetting the last reciprocal step, so the answer is 1/Ω instead of ohms.
- Assuming the full source voltage appears across each resistor in a series circuit.
- Splitting the voltage equally among series resistors that are not equal.
Exam tips
- A parallel total must be smaller than the smallest branch. If yours is not, look for an error.
- Series voltage drops must add up to the source voltage. It takes a few seconds to check.
Series and parallel circuits calculator
Questions people ask
How do you calculate total resistance in parallel?
Add the reciprocal of each branch resistance, then take the reciprocal of that sum: RT = 1 ÷ (1/R1 + 1/R2 + 1/R3). For two resistors you can use product over sum, (R1 × R2) ÷ (R1 + R2).
Is the current the same everywhere in a series circuit?
Yes. A series circuit has only one path, so the same current flows through every resistor. The voltage divides among the resistors in proportion to their resistance.
Why is total parallel resistance less than the smallest resistor?
Each branch adds another path for current, so the total current rises and the equivalent resistance falls. The total is always smaller than the smallest branch.
Are house circuits wired in series or in parallel?
Loads on a branch circuit, such as receptacles and lights, are connected in parallel so each one gets full voltage. The circuit conductors are in series with the loads, which is why long runs cause voltage drop.
Sources
About the tables: The exam is open book. These problems cite the 2026 NEC section and table so you practice finding them in your own book. We never print NEC text or tables.