---
title: "Moving-Coil Meter and DC Multimeter Interactive Lab | Sandbox Physics"
description: "Why does connecting a meter change the quantity you want to measure? A meter becomes part of the circuit."
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language: "en"
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  zh-CN: "https://sandboxphysics.com/zh/labs/moving-coil-multimeter/"
last_modified: "2026-10-28"
---

IN09 · The meter changes the circuit

# Moving-Coil Meter and DC Multimeter

**Why does connecting a meter change the quantity you want to measure?** A meter becomes part of the circuit. A voltmeter draws some current across the component, and an ammeter adds resistance along the current path. Their input networks change the voltage and current they read; the size of that change depends on the circuit and the selected range.

Connect physical probes, compare moving-coil and digital meters, and retain calibrated DC readings to measure loading and current burden.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A small simulated DC resistor circuit includes the actual meter input network. The moving-coil model uses an ideal radial field, linear spring, viscous damping, back emf and dissipative mechanical stops. Coil inductance, magnetic fringing, hysteresis, heating and contact resistance are omitted. Digital mode uses a finite input resistance or a shunt/fuse path and a generic clipped linear quantizer; it does not reproduce a manufacturer ADC. References and measurements are separate. Calibration uses observed zero and known span readings. No AC, RMS or resistance mode is modeled.

### What changed when the meter was connected?

$V/\mathrm V$

Grey is the ideal unconnected circuit reference; turquoise is the calibrated stored reading, or orange when invalid. These values keep their saved circuit and wiring while the apparatus previews new settings.

Raw detector readings and zero/span calibration

Saved readings

| Record | Channel | Raw value | Calibrated | Valid for target |
| --- | --- | --- | --- | --- |

Exports retain actual input resistors, probe nodes, bridge state, raw detector value, calibration observations, circuit solution, ideal reference, model version and seed.

Physics tutorial

## Include the meter in the circuit

**Background** A voltmeter adds a current path between two nodes. An ammeter occupies a path that previously carried current through a wire. Both change the circuit they observe.

**Why it matters** A precise detector can report a changed circuit very accurately. Calibration of the detector and disturbance of the measured circuit are separate questions.

Start with the essentials

- **Focus question**: Why does connecting a meter change the quantity you want to measure?
- **One-sentence intuition**: The meter resistance belongs in the circuit solution before its indication is interpreted.

### Core mathematical model

#### A radial field drives the same shaft as the pointer

$$
J\ddot\theta+b\dot\theta+\kappa(\theta-\theta_0)=K_t I_g,\qquad e_b=K_t\dot\theta
$$

The shaped poles give an ideal radial field at the two active coil sides. Positive coil current produces positive shaft torque. The back emf returns mechanical work to the electrical model; it vanishes when the pointer is stationary.

#### Two ways to extend a movement range

$$
\begin{aligned}R_{\mathrm{sh}}&=\frac{I_{g,\mathrm{FS}}R_g}{I_{\mathrm{FS}}-I_{g,\mathrm{FS}}}\\ R_{\mathrm{series}}&=\frac{V_{\mathrm{FS}}}{I_{g,\mathrm{FS}}}-R_g\end{aligned}
$$

A shunt carries the part of the terminal current that bypasses the coil. A series multiplier limits coil current in voltage mode. The current range exceeds the coil full-scale current; each displayed range uses its actual resistor values.

#### A voltage input changes the load

$$
V_{\mathrm{loaded}}=V_s\frac{R_L\parallel R_{\mathrm{in}}}{R_s+R_L\parallel R_{\mathrm{in}}}
$$

With the bridge closed, the voltage input and the load connect to the same two circuit nodes. The source resistance then sees a different parallel combination. Digital mode has a large but finite input resistance.

#### Reduce the saved raw reading with the saved reference

$$
q_{\mathrm{ind}}=q_{\mathrm{ref}}\frac{s-s_0}{s_{\mathrm{ref}}-s_0}
$$

The raw channel is pointer angle or ADC count. The zero and known-span signals come from separate stored calibration observations. The inverse does not use the hidden coil constant, spring stiffness or ADC gain.

### Common difficulties

#### More digits do not remove loading

**Typical misconception** A digital reading must be the voltage that existed before the meter was connected.

**Better mental model** The ADC measures the circuit with its input connected. A high input resistance makes its disturbance smaller, and the finite resistance still belongs in the circuit.

#### A reversed lead changes the sign

**Typical misconception** A negative reading means the passive load acquired negative resistance.

**Better mental model** The indication follows the red-to-black orientation. Reversing the probes reverses the detector signal; the resistor and its positive power dissipation are unchanged.

### Run the experiment

1. 01

   #### Watch a weak divider

   Choose The meter pulls voltage down, then Digital, with finite input.

   **What to observe:** The input network changes, the loaded node moves and the raw sensing mechanism changes from a rotating coil to an ADC display.

2. 02

   #### Move the actual probes

   Drag a probe between the feed, load and return contacts. Use the bridge to open or close the feed-to-load gap.

   **What to observe:** A snapped probe touches the selected physical post. The circuit is solved with those actual nodes, so a wrong connection can bypass the meter, disconnect the load or overload the input.

3. 03

   #### Compare current ranges

   Compare A sensitive current range and Less current burden.

   **What to observe:** The more sensitive range inserts more resistance. Its burden is the voltage across the whole meter input path, including a digital shunt and the extra series path.

4. 04

   #### Keep a reading before previewing another setup

   Keep this reading, move either probe and export CSV or JSON.

   **What to observe:** The saved reading retains its original raw channel, circuit, range resistors and zero/span calibration. A transient or overrange record carries an explicit invalid-target flag.

Physical conclusion

Keep the actual range network, contact nodes and raw detector reading together with the calibration.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why does a meter change the circuit?**](https://sandboxphysics.com/stories/instruments/electrical-meters/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)