Measurement of Resistance

Resistance-measurement methods

A voltmeter-ammeter method uses R = V/I but includes instrument loading. A two-wire ohmmeter includes lead and contact resistance. Four-wire or Kelvin measurement uses separate current and voltage-sense connections to reduce lead-drop error, particularly for low resistance. High-resistance measurements require control of leakage, guarding and environmental effects. Resistance measurements normally require the circuit to be de-energized and stored energy discharged using the equipment procedure. Do not connect an ohmmeter to an energized circuit.

Wheatstone bridge

Label the left series arm as R1 above R2 and the right arm as R3 above Rx. Apply excitation between the common top and bottom nodes; connect the null detector between the midpoints. At balance, R2/(R1 + R2) = Rx/(R3 + Rx), so R1 Rx = R2 R3 and Rx = R2 R3/R1. This formula depends on the stated labeling. At ideal balance detector current is zero; lead, contact and detector limitations still affect real measurements.

Worked example

R1 = 100 Ω, R2 = 200 Ω and R3 = 150 Ω. At balance Rx = 200 × 150/100 = 300 Ω. For a separate low-resistance measurement, a true 0.1 Ω resistor with two 0.02 Ω leads reads 0.14 Ω in an ideal two-wire method, a +40% lead error. A properly implemented four-wire measurement excludes most of these lead voltage drops.

Loading example

If a 1 kΩ resistor is measured by a 10 kΩ voltmeter in parallel, the parallel combination is 909.1 Ω. Whether the ammeter measures resistor current or combined current determines the correction; always draw the actual connections.

Quick check

1. Why use four wires? To separate current-carrying leads from voltage sensing.
2. Can the bridge formula be used without labeling arms? No.
3. What can corrupt high-resistance readings? Leakage paths, moisture and contamination.