Voltmeter Design is an All About Circuits worksheet on building and understanding an analog DC voltmeter from a sensitive meter movement. The current page, attributed to Tony R. Kuphaldt, lists 18 questions across six pages, with expandable answers and a PDF option. It combines calculations with laboratory work: selecting safe ranges, sizing series resistors, measuring coil resistance, wiring circuits, and examining galvanometer and PMMC construction. Open the original worksheet.
What this worksheet teaches
This is a design-oriented DC-circuits exercise, not a generic probe-placement handout. Its questions ask students to explain why an analog movement needs a multiplier resistor, calculate expected readings, construct circuits, compare calculated and measured values, and investigate the mechanism inside the instrument. It appears in All About Circuits’ DC Electric Circuits worksheet collection alongside voltage dividers, current dividers, ammeter design, Kirchhoff’s laws, and DC metrology.
- Format: 18 questions on six pages, according to the current worksheet page.
- Author attribution: Tony R. Kuphaldt.
- Answers: Revealed interactively on the web page; a PDF option is also provided.
- Level: Suitable for electrical-engineering students, electronics trainees, instructors, and hobbyists who can use Ohm’s law and basic laboratory equipment.
The page states that it is published under Creative Commons Attribution terms. Check the source’s current license notice and preserve attribution before reproducing its questions, diagrams, or answers.
How an analog voltmeter works
An analog voltmeter is a sensitive current meter with a carefully chosen resistance in series. The movement reaches full-scale deflection at a specified current, IFS, and has its own coil resistance, Rm. A multiplier resistor limits current so that the selected voltage range produces exactly that full-scale current.
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- The movement and multiplier are connected in parallel with the circuit or component being measured.
- The high resistance of the complete instrument keeps its current draw small.
- The scale is calibrated so the selected full-scale voltage corresponds to full-scale pointer movement.
A voltmeter is therefore different from an ammeter: an ammeter is placed in series and is designed for low resistance, while a voltmeter is placed in parallel and is designed for high resistance. Putting a conventional ammeter directly across a source can create a near-short circuit; putting a voltmeter in series normally prevents useful circuit operation.
Core design equations
For a desired full-scale voltage, the total resistance required by the movement and multiplier is:
Rtotal = VFS / IFS
The series multiplier is the total resistance minus the movement’s coil resistance:
Rseries = VFS / IFS − Rm
The instrument’s input resistance is:
Rin = Rm + Rseries
Resistor power must also be checked. At full scale, the multiplier dissipates:
P = IFS2Rseries = VseriesIFS
Select a component with suitable power and voltage margin, tolerance, and temperature stability; a mathematically correct resistance can still fail if its physical ratings are inadequate.
Meter sensitivity in ohms per volt
Analog-voltmeter sensitivity is the reciprocal of full-scale current:
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S = 1 / IFS
Use amperes for IFS. Sensitivity lets you find total input resistance directly:
Rin = S × Vrange
For a 50 µA movement, S = 20,000 Ω/V. A 10 V range therefore has approximately 200,000 Ω total input resistance; subtract Rm to obtain the external multiplier.
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Example: 10 V range
Suppose IFS = 100 µA and Rm = 1,000 Ω.
- Rtotal = 10 V / 100 µA = 100,000 Ω.
- Rseries = 100,000 Ω − 1,000 Ω = 99,000 Ω.
- At full scale, the multiplier dissipates (100 µA)2 × 99,000 Ω = 0.99 mW. A standard resistor with an appropriate voltage and power rating is sufficient electrically, subject to the instrument’s safety design.
Example: sensitivity and a 25 V range
For IFS = 50 µA, sensitivity is 20,000 Ω/V. A 25 V range needs 20,000 × 25 = 500,000 Ω total. The multiplier is 500,000 Ω − Rm; insert the measured movement resistance rather than assuming it is zero.
Why start on the highest manual range?
Question 1 lists manual ranges of 500, 250, 100, 50, 25, 10, and 5 V. Its answer is to begin at 500 V, observe the indication, and then move down to a range that gives better resolution. Starting high limits the chance that an unknown voltage will force excessive movement current.
This is a principle for a properly rated manual-range instrument, not permission to apply an unknown circuit to any 500 V setting. Confirm the meter’s maximum voltage, CAT category where applicable, probe insulation, and the circuit’s energy level. Auto-ranging digital multimeters select ranges electronically, but the same over-range reasoning remains useful.
What a direct 6 V connection can do
The worksheet warns that connecting a bare movement directly to a 6 V battery could drive destructive current and that reversed polarity causes reverse deflection. The current would be:
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I = V / Rm
Because a galvanometer coil often has low resistance, several volts can produce far more than its full-scale current. The pointer may slam into a stop (“peg”), stressing the mechanism; damage depends on the movement’s rating, duration, and construction, so it is not accurate to claim that every movement fails instantly. Reverse DC can drive the pointer backward and may likewise impact the opposite stop. Always include current-limiting resistance and verify polarity before energizing.
Measuring the movement’s coil resistance
The worksheet’s substitution method uses a regulated DC supply, a decade resistance box in series, the movement, and a known shunt resistor Rs.
- Adjust the decade box until the movement reaches a chosen deflection. Record the series setting as R1.
- Connect Rs in parallel with the movement.
- Readjust the decade box until the original deflection returns. Record the new setting as R2.
- Use the same supply voltage and keep the deflection identical for both readings.
Derivation
Initially, movement current is:
Im = VsRm / (R1 + Rm)
With the shunt, the parallel combination is:
Rp = Rm ∥ Rs = RmRs / (Rm + Rs)
The restored-deflection condition gives:
Im = VsRp / (R2 + Rp)
Equating the two currents, canceling the stable supply voltage, substituting the parallel-resistance expression, and simplifying yields the worksheet’s result:
Rm = RsR2 / (R1 − R2)
The formula requires R1 > R2. If that relationship is not observed, check the wiring, units, shunt placement, supply stability, and whether the same deflection was actually restored.
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On page 2, the worksheet asks students to connect theory with physical measurements. Its sequence is:
- Measure and record actual component values.
- Draw the schematic.
- Build the circuit.
- Compare every connection with the schematic before applying power.
- Calculate expected voltages and currents.
- Measure the circuit’s actual quantities.
- If the difference exceeds a few percent, recheck wiring and calculations.
The recommendation to use roughly 1 kΩ to 100 kΩ resistors is the worksheet author’s classroom guidance, except when deliberately demonstrating loading; it is not a universal component-selection rule. This exercise exposes resistor tolerance, supply sag, contact resistance, movement calibration, and the fact that a meter becomes part of the circuit.
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Meter loading and measurement error
A real voltmeter draws current. If a source has Thevenin voltage VTh and resistance Rsource, connecting a meter of resistance Rmeter produces:
Vmeasured = VTh × Rmeter / (Rsource + Rmeter)
Error becomes significant when the meter resistance is comparable with source resistance. A high-sensitivity analog meter reduces loading, while a low-sensitivity range or low-value multiplier increases it. This is why the worksheet treats very high- and low-value resistors as a special loading experiment.
Galvanometers and PMMC movements
Galvanometer
A galvanometer is a sensitive current-responsive movement that turns electromagnetic force into pointer deflection; it is not automatically a complete voltmeter. The worksheet invites students to research galvanometers or make a crude demonstration. One suggested approach adapts a loudspeaker voice-coil/cone assembly and uses a laser-and-mirror arrangement to make small motion easier to see. Such a demonstration can show deflection, but it will not necessarily provide useful accuracy, linearity, damping, calibration, or overload protection.
PMMC
PMMC means Permanent Magnet, Moving Coil. The movement resembles a small DC motor with restricted travel. Its principal parts include a permanent magnet, pole pieces and magnetic gap, moving coil, pointer, control springs, damping system, and mechanical zero adjustment. A basic PMMC movement is polarity-sensitive and normally intended for DC. AC measurement requires rectification or a movement designed for that service; a bare PMMC mechanism should not be assumed to read arbitrary AC correctly.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Multi-range design considerations
A multi-range analog voltmeter can switch separate multiplier resistors or sections of a resistor network. Every position must keep movement current at or below IFS; the switch must never bypass protective resistance during transition. Resistors need adequate voltage and power ratings, and the highest range must itself be within the instrument’s insulation and safety ratings. The worksheet’s visible material does not specify one complete switch topology, so these are general design requirements rather than a claimed worksheet circuit.
Common faults and recovery
Pointer pegs immediately
- Disconnect power at once.
- Check for a missing or bypassed multiplier, an incorrectly wired range switch, a range that is too low, or reversed polarity.
- With power removed, measure the intended series resistance and verify the source voltage.
- Reconnect only on the highest safe rated range.
Pointer barely moves
Look for excessive multiplier resistance, an incorrect full-scale-current assumption, a wrong decade-box unit, a low source voltage, or an unwanted series connection.
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Reading is below calculation
Check loading, resistor tolerance, supply sag, movement calibration, the assumed Rm or IFS, and breadboard contacts.
Reading is unstable
Investigate an unregulated supply, loose wiring, mechanical friction, inadequate damping, a noisy range switch, or thermal drift in the multiplier.
Coil formula gives an impossible value
Confirm that R1 and R2 use the same units, Rs is parallel with the movement, the supply remained stable, and the original deflection was restored.
Analog movement versus a digital multimeter
| Issue | Analog movement | Digital multimeter |
|---|---|---|
| Sensing | Pointer deflection proportional to movement current | Electronic measurement with numerical display |
| Range selection | Often manual; multiplier resistance is central to the design | Often auto-ranging or electronically selected |
| Polarity | Reverse connection can drive the pointer backward | Usually displays a negative sign |
| Overload | Mechanical pegging can damage the movement | Protection depends on the meter’s design and rating |
| Loading | Depends on sensitivity and selected range | Input resistance is commonly specified in megohms |
| Learning value | Makes current limiting, scaling, and loading visible | Convenient for routine measurements |
The worksheet uses analog hardware because its limitations reveal the underlying circuit principles. That does not make an analog meter universally preferable for field measurements.
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Safety checklist
- Use a movement, resistor, supply, leads, and switches rated for the intended voltage and energy.
- Verify polarity and the multiplier with power removed.
- Begin on the highest safe range, never merely the highest printed range.
- Inspect probe insulation and keep hands behind probe guards.
- For hazardous circuits, follow the applicable CAT rating and laboratory procedures; use one-hand practice where appropriate.
- Do not treat a classroom movement as a substitute for a certified test instrument.
Using the worksheet effectively
Work each calculation before revealing an answer, then build only low-energy circuits within your equipment ratings. Record actual resistor values, supply voltage, selected range, pointer indication, and calculated error. When results disagree, troubleshoot the circuit and assumptions rather than silently replacing measured values with nominal ones.
The Bottom Line
The worksheet’s central lesson is simple: an analog voltmeter is a calibrated, current-limited movement placed in parallel with a circuit. Determine its full-scale current and coil resistance, calculate the series multiplier for the required range, account for loading and power, and verify the design with safe measurements.
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