Calculate Voltmeter Series Resistor

Calculator and formulas for calculating the series resistor of a voltmeter

Series Resistor Calculator

Measuring Range Extension

Calculation of the series resistor to extend the measuring range of a voltmeter. Choose between meter resistance or meter current as input parameter.

Choose Input Parameter
Results
Series resistor Rs:
Power Ps:

Voltmeter Series Resistor

Voltmeter series resistor circuit

Circuit diagram: Voltmeter with series resistor

Purpose of Series Resistor
  • Measuring range extension for voltmeters
  • Voltage reduction for the meter movement
  • Enables measurement of higher voltages
  • Protection of the sensitive meter movement
Input Modes
Meter resistance: Direct resistance value of the meter movement
Meter current: Maximum current through the meter movement
Important Note
The series resistor forms a voltage divider with the meter movement. The input voltage is divided proportionally to the resistances.

Formulas for Series Resistor Calculation

Calculation via Meter Current

When the meter current is known:

\[R_s = \frac{U_{total} - U_m}{I_m}\]

Voltage drop across series resistor ÷ meter current

Calculation via Meter Resistance

When the meter resistance is known:

\[R_s = \left(\frac{U_{total}}{U_m} - 1\right) \cdot R_m\]

Voltage ratio determines series resistor

Voltage Divider Principle

The series resistor and meter movement form a voltage divider:

\[\frac{U_m}{U_{total}} = \frac{R_m}{R_m + R_s}\]
\[R_s = R_m \cdot \left(\frac{U_{total}}{U_m} - 1\right)\]

Practical Calculation Example

Example: Measuring range extension from 10V to 100V

Given: Voltmeter with Rm = 10kΩ, Um = 10V, desired measuring range: 100V

Solution using voltage divider formula
Calculate voltage ratio:
\[\frac{U_{total}}{U_m} = \frac{100V}{10V} = 10\]
Calculate series resistor:
\[R_s = \left(\frac{U_{total}}{U_m} - 1\right) \cdot R_m = (10 - 1) \cdot 10kΩ = 9 \cdot 10kΩ = 90kΩ\]
Meter current at full scale:
\[I_m = \frac{U_m}{R_m} = \frac{10V}{10kΩ} = 1mA\]
Power dissipation in series resistor:
\[P_s = I_m^2 \cdot R_s = (1mA)^2 \cdot 90kΩ = 0.09W = 90mW\]
Result: Series resistor Rs = 90kΩ with a power dissipation of 90mW.
The measuring range is successfully extended from 0-10V to 0-100V.
Calculation Verification
Total resistance: Rtotal = 10kΩ + 90kΩ = 100kΩ
Current at 100V: I = 100V ÷ 100kΩ = 1mA ✓
Voltage across meter: Um = 1mA × 10kΩ = 10V ✓
Voltage across series resistor: Us = 1mA × 90kΩ = 90V ✓
Practical Notes
• Series resistor must handle power dissipation
• Use precision resistor for accurate measurement
• Consider temperature coefficient
• Input resistance increases by factor 10

Theory and Practical Applications

Operating Principle

A series resistor for a voltmeter is used to extend the maximum measurable range. The series resistor is connected in series with the voltmeter and forms a voltage divider with the internal resistance of the voltmeter.

Important Properties
  • Voltage division: Input voltage is divided proportionally to the resistances
  • Same current: The same current flows through both resistances
  • Input resistance: Increases by the extension factor
  • Linearity: Linear scaling of the measuring range
Practical Applications
  • Digital multimeters: Voltage measurement in different ranges
  • Analog instruments: Range extension of mechanical meter movements
  • Oscilloscopes: Probe heads with 10:1 or 100:1 division
  • Mains voltage measurement: Safety isolation through high resistances
  • HV measurement technology: High voltage measurement with divider circuits
Symbol Directory
UtotalTotal voltage / Input voltage
UmVoltage across meter movement
RmResistance of meter movement
ImCurrent through meter movement
RsValue of series resistor
PsPower of series resistor
Important Notes
  • Series resistor must be precisely dimensioned
  • Consider power handling of series resistor
  • Temperature coefficient important for accuracy
  • Input resistance increases proportionally
  • Maintain safety distances for high voltage
Practical Tips
  • Use precision resistors (1% or better)
  • Pay attention to low temperature coefficient
  • Choose sufficient voltage rating
  • For RF: Consider inductance of resistor
  • Perform regular calibration

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