Compare potential differences with a potentiometer null method
Use a balanced potential gradient and a galvanometer zero reading to compare e.m.f.s or potential differences.
Section 10 · D.C. circuits
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 10. These original circuit diagrams and calculations are study aids; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use current, potential difference, resistance, energy and charge with consistent circuit directions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does zero galvanometer deflection indicate at potentiometer balance?
What you will learn
- Recall and use the potentiometer principle for comparing p.d.s
- Explain the galvanometer's role as a null detector
- Relate balance lengths to potential differences under the same gradient
A potentiometer compares voltage using a balance length
A potentiometer wire carrying a steady current can provide a uniform potential gradient along its length if the wire is uniform and operating conditions stay fixed. A sliding contact is moved until the wire segment p.d. matches the unknown source or component p.d.
At balance, the galvanometer shows zero current in the comparison branch. The unknown p.d. equals the p.d. along the measured balance length. With the same gradient, p.d.s are proportional to their balance lengths: V₁/V₂ = l₁/l₂.
A galvanometer detects the null condition
A sensitive galvanometer indicates both the direction and presence of a small current in the test branch. At the null point it reads zero, so the comparison branch draws no current from the unknown source in the ideal method.
A null comparison avoids loading the unknown source during the balanced measurement. Keep the potentiometer-wire current and gradient unchanged when comparing lengths; if the gradient changes, the simple ratio no longer compares the same volts per unit length.
Pause and explain
On the same gradient, what happens to balance length if the compared p.d. doubles?
Worked example
Two sources balance at lengths 0.30 m and 0.45 m on the same potentiometer wire. The first has e.m.f. 1.2 V. Find the second.
Show the worked solution
- The gradient is the same, so ε₁/ε₂ = l₁/l₂.
- ε₂ = 1.2 × 0.45/0.30.
- Check the longer balance length corresponds to larger e.m.f.
Answer ε₂ = 1.8 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.
On a fixed potentiometer gradient, 0.25 V balances at 0.20 m. Find the balance length for 0.60 V.
Give me a hint
Use direct proportionality between p.d. and length at the same gradient.
Compare my reasoning
- The voltage ratio is 0.60/0.25 = 2.4.
- l₂ = 2.4 × 0.20 m.
- State the length.
0.48 m.
Look for these in your work
- Same gradient assumed
- Ratio calculated
- Length found
An unknown source balances at 0.35 m. A 1.4 V reference balances at 0.50 m on the unchanged wire. Find the unknown e.m.f.
Give me a hint
Use εunknown/εreference = lunknown/lreference.
Compare my reasoning
- εunknown/1.4 = 0.35/0.50.
- εunknown = 1.4 × 0.70.
- State volts.
0.98 V.
Look for these in your work
- Length ratio formed
- Voltage calculated
- Unit stated
The galvanometer reads zero at a potentiometer balance. Explain why this helps compare an unknown source without drawing current from it at balance.
Give me a hint
Relate the null reading to equal potential and branch current.
Compare my reasoning
- At balance the sliding contact and unknown source terminals are at equal potential.
- With no p.d. across the comparison branch, its current is zero.
- The unknown source is therefore not supplying current to the detector branch at the null point.
The zero indicates equal p.d. at the comparison point; no current is drawn from the unknown branch at balance, reducing loading.
Look for these in your work
- Equal potential identified
- Zero branch current reasoned
- Loading benefit stated
Common mistakes
- Assuming galvanometer zero means no current in the potentiometer wire
- Changing the wire current between balance measurements without recalibration
- Using balance-length ratios when the potential gradient changed
What can you explain now?
What does zero galvanometer deflection indicate at potentiometer balance?
Compare with the explanation
No current flows in the comparison branch
The potentials match at the balance point.
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Make it stick
Why is a zero-current balance useful for comparing a source's e.m.f.?
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.