Current measurement, shunts & burden voltage
A current measurement requires the meter to enter the branch, so the current path is no longer the original circuit. Model the finite insertion resistance, derive current error and burden voltage, understand why range choice can change the circuit, distinguish shunt resistance from the full instrument burden, and use safer alternative methods when direct insertion is too invasive.
- Explain why current measurement changes circuit topology by inserting the meter in series with the branch.
- Derive measured current for a Thévenin source, load path and finite meter insertion resistance.
- Derive the relative current error caused by meter insertion and connect it to burden voltage.
- Explain why the instrument's complete burden can exceed the idealized sensing-shunt drop and why the actual specification is model/range dependent.
- Analyze how current range selection can change shunt/insertion behavior and therefore change the measurand.
- Use limiting cases and power checks to validate current-measurement calculations.
- Recognize when measuring voltage across an existing known sense resistor is less invasive than inserting a current input.
- Apply fuse, jack, current-limit and instrument-manual checks without assuming that a fuse makes every current measurement safe.
If an ammeter is supposed to measure current, why can changing the current range change the current itself?
Because a current measurement is an insertion measurement. The meter must enter the branch, and its current path is not an ideal short. The branch being measured therefore becomes a new circuit.
03.1Current measurement is a topology change
A voltmeter is placed across two existing nodes. An ammeter requires the branch to be opened and the meter inserted into the current path. The exact current that existed before insertion is therefore not guaranteed to survive the measurement unchanged.
Represent the rest of the branch by a Thévenin source VTH driving an effective path resistance RP. In the first model, represent the meter current path by a finite insertion resistance RM.
Figure 3.1 — When available voltage is small, burden voltage becomes critical
Without the meter, 100 mV across 100 Ω would give 1.000 mA. Inserting a 10 Ω measurement resistance reduces the current to 0.909 mA and consumes about 9.09 mV of the available voltage.
03.2Derive the current before and after inserting the meter
Before insertion:
After insertion:
The relative insertion error, referenced to the original current, is
When RM≪RP,
This is the current-measurement analogue of voltmeter loading: the relevant quantity is again a resistance ratio, but now the meter resistance should be very small rather than very large.
03.3Burden voltage is the voltage consumed by the measurement path
In the simple insertion-resistance model, the meter develops
For the Figure 3.1 example:
The current error is 9.09%. Notice that the burden voltage is not merely a nuisance voltage “inside the meter”: it is voltage no longer available to the original branch.
A real instrument can include a sensing shunt, fuse, protection, switching and wiring. Therefore the complete burden seen by the circuit can differ from the drop across the sensing element alone.
03.4Turn an allowed current error into a maximum insertion resistance
Require
Solving for the meter insertion resistance:
If the original branch path is 500 Ω and the allowed current error is 0.1%:
This immediately tells you whether a proposed current range is electrically acceptable before making the measurement.
03.5Range choice can change the measurand
Different current ranges can use different current paths, shunts or switching configurations. A range with better displayed resolution may also present a different burden to the circuit. The exact trade-off is instrument dependent.
Consider a 1 V source driving an original 100 Ω path. Compare two hypothetical meter ranges:
Both can be “accurate ammeter ranges” in the sense of internal conversion accuracy, yet one perturbs this particular circuit far more than the other.
Autoranging can also change the active range during a reading. When burden matters, record the range or use a controlled range if the instrument and procedure allow it.
03.6Power and heating provide another independent check
The insertion path dissipates power:
For 20 mA through an equivalent 5 Ω measurement path:
The power check is useful because it ties together current, burden voltage and insertion resistance. It also reminds us that current ranges and fuses have finite ratings and thermal limits.
03.7An alternative: measure voltage across an existing sense resistor
If a known resistor already lies in the current path, current can sometimes be inferred from its voltage drop:
This avoids opening the branch and inserting the current input. It is not perfectly non-invasive: the voltmeter input appears in parallel with the sense resistor and slightly changes its effective resistance. But when RIN≫Rsense, that disturbance can be far smaller than the burden of a direct current measurement.
Example: a 10 Ω sense resistor with 50.0 mV across it implies 5.00 mA. A 10 MΩ voltmeter placed across 10 Ω changes the effective resistance by only about one part per million.
The final uncertainty still depends on voltage-measurement accuracy and resistor value/tolerance; those contributions belong in the complete uncertainty budget later.
03.8Polarity, jacks, fuses and ratings are part of the measurement model
A negative current reading normally means the actual current flows opposite to the instrument’s positive reference direction. It is not an error by itself.
Before a direct current measurement:
- Identify the expected current order of magnitude and source capability.
- Select the correct current jack and function according to the manual.
- Check the current range, fuse type/rating and any time limit stated for high-current ranges.
- Open the branch and insert the meter in series; never “probe across” the source as in voltage mode.
- Respect the meter, lead and installation-category ratings.
- After the current measurement, restore the leads before returning to voltage measurements.
03.9Mastery exercises
- A 5 V Thévenin source drives a 1 kΩ total path. Inserting the meter adds 10 Ω. Find original current, measured current, current error and burden voltage.
- A 100 mV source drives 100 Ω. Compare the current before and after inserting 10 Ω.
- An original path is 500 Ω. What maximum meter insertion resistance keeps current error below 0.1%?
- A 1 V source drives 100 Ω. Compare hypothetical current ranges with RM=0.1 Ω and RM=10 Ω.
- A 10 Ω sense resistor already in circuit has 50.0 mV across it. Estimate the current. Why can a voltage measurement be less invasive here?
- Calculate meter-path dissipation for 20 mA through 5 Ω.
- The display reads −3.2 mA. What can be concluded about current direction relative to the meter reference?
- Why must you check the actual current-range burden specification rather than infer it only from the displayed resolution?
Solutions
1. I0=5.000 mA; IM=5/1010=4.9505 mA; error≈0.990%; VB≈49.5 mV.
2. I0=1.000 mA; IM=0.9091 mA; error=9.09%; VB≈9.091 mV.
3. RM≤[0.001/0.999]·500 Ω≈0.5005 Ω.
4. RM=0.1 Ω gives 9.990 mA, 0.0999% error and ≈0.999 mV burden. RM=10 Ω gives 9.091 mA, 9.09% error and ≈90.91 mV burden.
5. I=50.0 mV/10 Ω=5.00 mA. A high-resistance voltmeter placed across an already-existing low-value sense resistor can disturb the branch far less than adding a current-input resistance in series.
6. 2.0 mW.
7. Current flows opposite to the meter’s defined positive direction; magnitude is 3.2 mA within the assumptions of the measurement.
8. Resolution describes displayed increment, while burden depends on the actual current-path implementation and range. The two are not the same specification.
Chapter 04 will turn to resistance, continuity, electrical reference and grounding: what an ohmmeter actually excites, why in-circuit paths matter, and why “ground” does not always mean earth.