What this page is for
These formulas help diagnose DVM meter loading error during pipe-to-electrolyte potential measurements. When the contact or external circuit resistance is high, the meter input resistance becomes part of a voltage-divider circuit and pulls the displayed reading toward zero (less negative) compared with the true polarized potential.
In practice, meter loading is most likely in dry soil, gravel, poor reference electrode contact, or other high-resistance measurement conditions. The formulas below are used to model the divider effect, estimate external resistance, correct the true potential from two readings, and calculate percent error.
Meter loading formulas
1) Meter loading (voltage divider)
2) Solve for external/contact resistance
3) Two-reading true-potential correction
Tip: If both readings are negative, \(\frac{V_h}{V_l}\) can be computed using signed values because the negatives cancel.
4) Percent error (magnitude)
Practice problems
When measuring pipe-to-electrolyte potential, the DVM displays a value that is less negative than expected.
What condition most directly causes meter loading error?
Reveal solution
Use (concept):
Meter loading becomes significant when the external/contact resistance \(R_{circ}\) is high and approaches the meter input resistance \(R_m\). Then the divider fraction becomes noticeably less than 1 and the measured value is pulled toward 0 (less negative).
True polarized potential \(E_{true}=-1.200\,\text{V}\). Meter \(R_m=10\,\text{M}\Omega\). External resistance \(R_{circ}=2\,\text{M}\Omega\).
What will the meter read (approx.)?
Reveal solution
Use:
You switch from a 10 MΩ DVM to a 100 MΩ electrometer and the reading becomes noticeably more negative.
What is the best interpretation?
Reveal solution
Key idea:
Increasing \(R_m\) reduces loading error.
Reasoning:
If the reading becomes more negative when \(R_m\) increases, the earlier 10 MΩ reading was being pulled toward 0 by the divider effect, and the higher-impedance meter is closer to \(E_{true}\).
You plan to use the two-reading true-potential correction method.
What must be different between the two measurements?
Reveal solution
Use (concept):
You must take two readings with two different meter input resistances (\(R_l\) and \(R_h\)) to create a solvable system.
A measurement gives \(V_m=-0.900\,\text{V}\) using \(R_m=10\,\text{M}\Omega\). You believe \(E_{true}=-0.950\,\text{V}\).
What is \(R_{circ}\) (approx.)?
Reveal solution
Use:
You are measuring pipe-to-soil potential in very dry/high-resistivity conditions.
Which action most directly reduces meter loading error?
Reveal solution
Use (concept):
Reasoning:
Increasing \(R_m\) increases the divider fraction and moves \(V_m\) closer to \(E_{true}\).
Consider the relative sizes of \(R_m\) and \(R_{circ}\).
When is meter loading error most likely?
Reveal solution
Rule of thumb:
Loading error becomes significant when \(R_{circ}\) approaches \(R_m\).
Reasoning:
If \(R_m \gg R_{circ}\), then \(R_m/(R_m+R_{circ}) \approx 1\) and loading is minimal. If \(R_{circ}\) is large, the fraction drops and the reading is biased toward 0.
True potential is \(-1.500\,\text{V}\). Meter reads \(-1.200\,\text{V}\) due to loading.
What is the magnitude of the percent error (approx.)?
Reveal solution
Use:
You suspect loading error during a survey.
What quick check is most appropriate?
Reveal solution
Best check:
Repeat the measurement with a much higher input resistance meter/electrometer and observe whether the reading shifts more negative.
Why:
If \(V_m\) changes meaningfully as \(R_m\) changes, a voltage-divider loading error is strongly indicated.
You are using the two-reading true-potential correction method.
How is \(K\) defined?
Reveal solution
Where \(R_l\) is the lower meter input resistance and \(R_h\) is the higher meter input resistance.