Internal DMM Resistance Calculator

Calculate the internal resistance (input impedance) of a voltmeter to understand its loading effect on your circuits.

Voltage Distribution Chart

Visual representation of the voltage drop across the series resistor vs. the DMM.

What is DMM Internal Resistance?

The internal resistance of a Digital Multimeter (DMM), often called input impedance, is a critical parameter that determines how much the meter affects the circuit it is measuring. An ideal voltmeter would have infinite internal resistance, meaning it could measure a voltage without drawing any current from the circuit. However, real-world DMMs have a finite, though very high, internal resistance. When you connect a DMM to a circuit, this internal resistance is placed in parallel with the component you’re measuring, creating a new current path. This can alter the circuit’s behavior, a phenomenon known as the “loading effect.” To accurately calculate the internal DMM resistance (r) is to understand and predict this effect, especially in high-impedance circuits where the loading can cause significant measurement errors. Most modern DMMs have an internal resistance of 1, 10, or 11 Megaohms (MΩ).

The Formula to Calculate Internal DMM Resistance

We can determine the internal resistance of a DMM by using a simple test circuit composed of a stable voltage source, a known series resistor, and the DMM itself. By measuring the voltage drop, we can use a variation of Ohm’s Law and the voltage divider principle to find the DMM’s resistance. The formula used by this calculator is:

R_dmm = R_S * (V_dmm / (V_S – V_dmm))

This equation effectively compares the voltage measured by the DMM to the voltage dropped across the known series resistor. To learn more about basic circuit principles, see our guide on the DMM internal resistance formula.

Description of Variables

Variable	Meaning	Unit	Typical Range
R_dmm	Internal Resistance of the DMM	Ohms (Ω)	1 MΩ – 11 MΩ
R_S	Known Series Resistor	Ohms (Ω)	100 kΩ – 10 MΩ
V_S	Source Voltage (Open Circuit)	Volts (V)	1 V – 30 V
V_dmm	Voltage Measured by DMM	Volts (V)	0 V – V_S

Practical Examples

Example 1: Standard 10 MΩ DMM

Suppose you have a power supply with an open-circuit voltage of 9V. You place a known 10 MΩ resistor in series with your DMM and measure the voltage across the DMM’s terminals.

• Inputs:
  • Source Voltage (V_S): 9 V
  • Series Resistor (R_S): 10 MΩ
  • Measured Voltage (V_dmm): 4.5 V
• Calculation:
  • R_dmm = 10,000,000 * (4.5 / (9 – 4.5))
  • R_dmm = 10,000,000 * (4.5 / 4.5)
  • Result: R_dmm = 10,000,000 Ω or 10 MΩ

This result is expected, as a series resistor of the same value as the DMM’s internal resistance creates a perfect voltage divider, halving the source voltage. For more on this, check out our article on how to measure DMM internal resistance.

Example 2: High-Impedance Circuit Measurement

Let’s see how a DMM can “load” a circuit. Imagine you are trying to measure the voltage across a sensitive component that has a high resistance, which we’ll model with a 1 MΩ series resistor. Your DMM has an internal resistance of 1 MΩ. The source voltage is 12V.

• Inputs:
  • Source Voltage (V_S): 12 V
  • Series Resistor (R_S): 1 MΩ
  • Measured Voltage (V_dmm): 6 V
• Calculation:
  • R_dmm = 1,000,000 * (6 / (12 – 6))
  • Result: R_dmm = 1,000,000 Ω or 1 MΩ

The DMM reads 6V, but the actual voltage across that point *without* the meter would be much closer to 12V. The meter’s low resistance (relative to the circuit) has significantly loaded the circuit and altered the voltage, leading to a 50% measurement error.

How to Use This Internal DMM Resistance Calculator

1. Measure Source Voltage (V_S): Use your DMM to measure the voltage of your power source directly. This gives you the open-circuit voltage. Enter this value into the “Source Voltage” field.
2. Select a Series Resistor (R_S): Choose a resistor with a known value. A good rule of thumb is to select a resistor close to the expected internal resistance of your DMM (e.g., 1 MΩ or 10 MΩ). Enter its value and select the correct unit (Ω, kΩ, or MΩ).
3. Connect the Circuit: Connect the series resistor between the positive terminal of your power source and the positive probe of your DMM. Connect the negative probe to the negative terminal of the source.
4. Enter Measured Voltage (V_dmm): Record the voltage displayed on the DMM and enter it into the “Measured Voltage” field.
5. Interpret the Results: The calculator will instantly calculate the internal DMM resistance (r) and display it. The intermediate values provide insight into the circuit’s behavior, such as the loading error introduced by the meter. You can learn about other measurement techniques in our guide to the ammeter internal resistance.

Key Factors That Affect the Calculation

• Series Resistor Tolerance: The accuracy of your R_S value directly impacts the result. Use a resistor with a low tolerance (e.g., 1%) for best results.
• Voltage Source Stability: A fluctuating power source will lead to inconsistent V_S and V_dmm readings, making the calculation unreliable. Use a regulated DC power supply.
• DMM Accuracy: The fundamental accuracy of the DMM you are testing will influence the V_dmm reading.
• DMM Range Setting: Some DMMs have different input impedances on different voltage ranges. Perform the test on the range you most commonly use. Understanding the voltmeter loading effect is key.
• Connections: Poor connections or long leads can add small, unwanted resistances to the circuit. Ensure all connections are firm and clean.
• Temperature: Extreme temperatures can affect the performance of both the DMM and the components in your test circuit.

Frequently Asked Questions (FAQ)

1. Why isn’t a DMM’s internal resistance infinite?

To measure voltage, the DMM’s internal circuitry requires a very small amount of current to operate. Since current must flow, the resistance cannot be infinite according to Ohm’s Law (R = V/I). The goal is to make this current draw as negligible as possible.

2. What is a “good” value for DMM internal resistance?

Higher is always better. Most modern DMMs have an input impedance of 10 MΩ, which is high enough for most electronics work. For very high-impedance circuits (like those in some sensors or amplifiers), a DMM with 1 GΩ or higher may be needed.

3. What is the “voltmeter loading effect”?

This is the error caused by the voltmeter itself altering the circuit it is measuring. By drawing current, the DMM acts like another resistor in the circuit, changing voltages and currents from their original values. This effect is more pronounced in high-impedance circuits.

4. How do I choose the best series resistor (R_S)?

For the most accurate result with this method, choose a series resistor with a value close to the expected internal resistance of the DMM. This makes the voltage division close to 50%, which minimizes the impact of measurement inaccuracies in V_dmm.

5. What happens if the measured voltage is very close to the source voltage?

If V_dmm is close to V_S, the denominator in the formula (V_S – V_dmm) becomes very small, making the calculation highly sensitive to small measurement errors. This typically happens when your series resistor (R_S) is much smaller than the DMM’s internal resistance.

6. How does this differ from an ammeter’s internal resistance?

An ideal ammeter has zero internal resistance, as it is placed in series to measure current and should not impede it. A voltmeter is the opposite, placed in parallel with a component and designed to impede current flow as much as possible. Our article on DMM resistance measurement covers more differences.

7. Is a higher internal resistance always better?

For a general-purpose voltmeter, yes. A higher internal resistance means the meter will have less of a loading effect on a wider range of circuits, leading to more accurate measurements.

8. How accurate is this calculator?

The calculator’s mathematical accuracy is perfect. The accuracy of your final result depends entirely on the precision of your input values (V_S, R_S, and V_dmm).