Add resistances in one series path
Calculate a series resistance total and distinguish it from a current shared by all loads.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recognize an unbranched series path.
- Convert resistance units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many ohms are in 0.5 kΩ?
What you will learn
- Calculate combined resistance of two or more series resistors.
- Find a missing positive resistance from a supplied total.
Add the actual series values
For resistors in series, the combined resistance is Rtotal = R1 + R2 + … . A 3 Ω resistor and a 7 Ω resistor in the same path give 10 Ω. Each additional positive resistance increases the total. Do not average the values or use the parallel rule.
Convert all values to one unit before adding: 0.5 kΩ is 500 Ω, so it and 250 Ω total 750 Ω. The physical order of the same series resistors does not change their sum in this model, although it changes where individual components appear in the diagram.
Check an unknown value
Subtract known series resistances from a supplied total to find a missing resistance. A 12 Ω total containing 3 Ω and 4 Ω leaves 5 Ω. A negative inferred value would contradict a model made only of the stated ordinary positive resistors; it signals an inconsistent total, units or connection assumption.
The current through each series resistor is the same in a steady path. At a fixed ideal source p.d., adding positive series resistance reduces the common current. These statements concern different quantities: resistance adds, while the current does not add across series loads.
Sources for this lesson
Pause and explain
A 12 Ω series total contains 3 Ω and 4 Ω plus an unknown resistor. What is the unknown?
Worked example
Find the equivalent resistance of 3 Ω, 4 Ω and 5 Ω in series.
Show the worked solution
- The components share one unbranched path.
- Add their resistances in ohms.
- 3 + 4 + 5 = 12 Ω.
Answer 12 Ω.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the combined resistance of 3 Ω, 4 Ω and 5 Ω in series.
Give me a hint
Add every component in the one path.
Compare my reasoning
- All resistances are already in ohms.
- Rtotal = 3 + 4 + 5.
- Rtotal = 12 Ω.
12 Ω.
Look for these in your work
- Use the series rule.
- Include all three values.
Find the total of 0.5 kΩ and 250 Ω in series.
Give me a hint
Convert the prefixed resistance before adding.
Compare my reasoning
- 0.5 kΩ = 500 Ω.
- 500 + 250 = 750.
- The combined resistance is 750 Ω or 0.75 kΩ.
750 Ω or 0.75 kΩ.
Look for these in your work
- Use consistent units.
- Do not average resistances.
An alleged 5 Ω series total contains 3 Ω, 4 Ω and one ordinary positive resistor. Find the implied unknown and assess the data.
Give me a hint
Subtract known contributions and compare the sign with the model.
Compare my reasoning
- Known resistance totals 7 Ω.
- The implied unknown is 5 − 7 = −2 Ω.
- That contradicts the stated positive-resistor series model.
Implied −2 Ω; the supplied data or series assumption is inconsistent.
Look for these in your work
- Show the subtraction.
- Reject a negative ordinary-resistor interpretation.
Common mistakes
- Series resistance adds, not averages.
- Convert kΩ and Ω first.
- A negative ordinary-resistor result needs an inconsistency check.
What can you explain now?
What is the series resistance rule?
Compare with the explanation
Add the component resistances.
Every stated positive series resistor contributes to the total.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Add series resistances in consistent units and check missing-value signs.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.