Combine the e m f of sources in series
Add aiding source rises and subtract opposing ones using their labelled polarities.
Core and Extended; Physics 0625, 2026–2028. Use the stated source, operating conditions and meter ranges. Written practice is self-checked.
Before you begin
- Read long positive and short negative plates.
- Add signed numbers consistently.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which cell-symbol terminal is positive?
What you will learn
- Calculate combined e.m.f. of several series sources.
- Keep source polarity and ideal-terminal assumptions explicit.
Choose a traversal direction
For aiding sources in series, each is connected so its negative terminal leads toward the next source positive terminal in the assembly, giving additive rises between the outer terminals. Three aiding 1.5 V cells give a combined e.m.f. of 4.5 V. Include all supplied sources, not just the nearest one.
More generally, choose one traversal direction through the source assembly. A passage from a source negative to positive contributes a rise; a positive-to-negative passage contributes a fall. Add those signed contributions. A reversed cell therefore opposes the others rather than increasing the total by its magnitude.
Distinguish the specified source account
Two aiding 1.5 V sources and one opposing 1.5 V source give 1.5 V net in the direction of the aiding pair. A zero net sum does not mean individual source e.m.f.s are zero. It means their signed rises and falls balance under the model.
Combined e.m.f. is a source work-per-charge account. Terminal p.d. under load can differ for non-ideal sources with internal resistance. Introductory questions assume ideal sources or ask for combined e.m.f.; do not present a diagram calculation as a practical instruction to connect arbitrary real power supplies together.
Pause and explain
Three 1.5 V cells contain two aiding and one opposing contribution. What is the net e.m.f.?
Worked example
Three 1.5 V cells are in series, with two aiding and one opposing the chosen direction. Calculate the combined e.m.f.
Show the worked solution
- Assign +1.5 V to each aiding cell.
- Assign −1.5 V to the opposing cell.
- Add 1.5 + 1.5 − 1.5 = 1.5 V.
Answer 1.5 V net in the aiding-pair direction.
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.
Calculate combined e.m.f. of three aiding 1.5 V cells.
Give me a hint
All rises have the same sign.
Compare my reasoning
- Choose the aiding traversal direction.
- Add 1.5 + 1.5 + 1.5.
- The total is 4.5 V.
4.5 V.
Look for these in your work
- Include all three sources.
- State volts.
Sources contribute +6 V, +3 V and −2 V along a chosen traversal. Find the net e.m.f. and direction.
Give me a hint
Add the signed contributions, retaining the reference.
Compare my reasoning
- The aiding total is 6 + 3 = 9 V.
- Subtract the opposing 2 V.
- The net is +7 V in the chosen direction.
+7 V in the chosen traversal direction.
Look for these in your work
- Use the opposing sign.
- State the reference direction.
Two equal 2 V sources oppose in an ideal diagram. A learner says both sources have no e.m.f. Explain the distinction.
Give me a hint
Compare individual work-per-charge accounts with the assembly sum.
Compare my reasoning
- Each source still has 2 V e.m.f.
- Their signed contributions are +2 V and −2 V.
- The combined net is 0 V without eliminating either individual source.
Net 0 V; each source still has its individual 2 V e.m.f.
Look for these in your work
- State individual and net values.
- Do not infer real-source connection suitability.
Common mistakes
- Use polarity rather than adding every magnitude.
- Zero net e.m.f. does not make each cell zero.
- Terminal p.d. under load needs the stated source model.
What can you explain now?
How are aiding series e.m.f.s combined?
Compare with the explanation
Add their values.
Aiding rises have the same sign in the chosen traversal.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Choose a direction and add aiding and opposing source e.m.f.s with 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.