# Series, parallel and combination circuit calculations

> In a series circuit the resistances add and the same current flows through each one. In a parallel circuit every branch gets the full voltage, and the total resistance is the reciprocal of the sum of the reciprocals, which is always smaller than the smallest branch.

Exams: Journeyman Electrician, Master Electrician, Residential Wireman. Electrical theory.

## Formula

    Series: RT (Ω) = R1 + R2 + R3
    Parallel: RT (Ω) = 1 ÷ (1/R1 + 1/R2 + 1/R3)
    Two in parallel: RT (Ω) = (R1 × R2) ÷ (R1 + R2)

## Variables

- **RT**: Total (equivalent) resistance (Ω)
- **R1, R2, R3**: Individual resistances (Ω)
- **E**: Source voltage, or the voltage across one part (V)
- **I**: Current (A)

## Open your 2026 NEC to

- Chapter 9, Table 8: Conductor resistance per 1,000 ft; circuit conductors act as resistance in series with the load

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.

## 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?

1. Series resistances add: RT = 31 + 33 + 37 = 101 Ω.
2. The same current flows through every part of a series circuit: I = E ÷ RT = 24 ÷ 101 = 0.2376 A.
3. Voltage across R2: E2 = I × R2 = 0.2376 × 33 = 7.84 V.

**Answer: 7.84 V**

## How to solve it on the exam

1. Sketch the circuit and mark which resistors share one path (series) and which connect across the same two points (parallel).
2. Reduce each parallel group to one equivalent resistance: product over sum for two, reciprocals for three or more, R ÷ n for n equal resistors.
3. Add the series resistances, including any parallel equivalents, to get RT.
4. Find the total current with I = E ÷ RT.
5. 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.

## 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

- [TDLR: Electrician examination information](https://www.tdlr.texas.gov/electricians/elecexam.htm)
- [PSI: Texas electrician Candidate Information Bulletin](https://test-takers.psiexams.com/api/content/bulletin/1682)

Interactive practice: https://texaselectricianexam.com/calculations/series-parallel-circuits/