Calculate source work per charge as electromotive force
Use the e.m.f. equation with a named source work account and distinguish it from a component-only work value.
Section P4.2.3 · Electromotive force and potential difference
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
- Define source e.m.f.
- Convert joules and coulombs and divide quantities.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which unit is equivalent to J/C?
What you will learn
- Use e.m.f. = W/Q for source electrical work.
- Match consistent energy and charge units to the source boundary.
Apply the source equation
For the stated source account, e.m.f. = W/Q, where W is electrical work done by the source and Q the charge moved around the complete circuit. In J and C, the result is V. If 18 J of source work accompanies 3 C, the e.m.f. is 6 V. The historical symbol E for e.m.f. is distinguished here from an electrical-energy symbol by naming the source quantity.
Use a non-zero charge amount for the ratio. A zero-work, zero-charge interval gives 0/0 and does not determine a unique e.m.f. A source can retain non-zero e.m.f. even though no charge passed during a selected open-circuit interval.
Keep the work boundary consistent
A lamp-only work value is not automatically the total source work. The source may supply energy to other components or transfer some internally. Identify which energy account is actually given before dividing by charge and naming the result e.m.f.
Convert prefixed units before the calculation. 24 mJ of source work for 4 mC gives (24 × 10⁻³)/(4 × 10⁻³) = 6 V. Matching prefixes cancel here, but unlike prefixes need their separate conversion factors. The result is a work-per-charge value, not total work or current.
Sources for this lesson
Pause and explain
24 mJ of source work accompanies 4 mC. What e.m.f. follows?
Worked example
A source does 18 J of electrical work while 3 C passes around the complete circuit. Calculate its e.m.f.
Show the worked solution
- Use e.m.f. = W/Q for the source account.
- W = 18 J and Q = 3 C.
- 18/3 = 6 V.
Answer 6 V.
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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 source e.m.f. for 18 J of work and 3 C passed charge.
Give me a hint
Use the source's work and the same charge account.
Compare my reasoning
- E.m.f. = W/Q.
- 18/3 = 6.
- The unit J/C is V.
6 V.
Look for these in your work
- Name the source boundary.
- State volts.
Calculate e.m.f. for 24 mJ and 4 mC, and for 12 J and 2 mC in separate source accounts.
Give me a hint
Convert both quantities in each trial before dividing.
Compare my reasoning
- 0.024/0.004 = 6 V.
- 12/0.002 = 6000 V.
- Only the first trial has matching prefixes to cancel.
6 V; 6000 V.
Look for these in your work
- Treat both accounts separately.
- Do not cancel unlike scales.
An open circuit has no passed charge or source work during a chosen interval. Does W/Q establish zero e.m.f.?
Give me a hint
Check whether the ratio is defined for Q = 0.
Compare my reasoning
- The supplied interval gives W = 0 and Q = 0.
- The ratio 0/0 is indeterminate.
- The source e.m.f. requires other suitable information.
No; 0/0 does not determine e.m.f., which can remain non-zero.
Look for these in your work
- Identify the indeterminate ratio.
- Keep source ability separate from interval transfer.
Common mistakes
- Use source work, not an isolated component's work.
- Convert energy and charge prefixes separately.
- An open interval's 0/0 does not determine e.m.f.
What can you explain now?
What quantity belongs in W when finding source e.m.f.?
Compare with the explanation
Electrical work done by the source.
The formula requires the source account rather than an arbitrary component-only energy.
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Make it stick
Calculate source e.m.f. from a matching non-zero work–charge account with consistent units.
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.