Unit 4 — Calibration Procedure and Calculations

TM-CAL-009 — Open Handout TM Chapters: Chapter 5, Appendix A ELOs: Execute calibration procedure; compute error and determine pass/fail Estimated time: 30 minutes

Step 1: Read the TM

Open TM-CAL-009. Read Chapter 5 and Appendix A completely.

Then come back here.

Chapter 5 — Calibration Procedure

  1. Connect unknown resistor to Rx terminals.
  2. Set decade box (Rs) to estimated value of unknown.
  3. Briefly close galvanometer switch. Observe deflection direction.
  4. Adjust Rs: if galvanometer deflects right, Rs is low (increase); if left, Rs is high (decrease).
  5. Iterate until galvanometer reads zero with switch held closed (null balance).
  6. Calculate: Rx = Rs × (Rb / Ra).
  7. Read Rs value from decade box. Apply ratio-arm correction if Rb ≠ Ra.

Appendix A — Formulas

Unknown resistance at null
Rx = Rs × Rb / Ra

Equal-arm bridge (Ra = Rb)
Rx = Rs

Bridge sensitivity (for galvanometer selection)
IG = E × ΔR / (4 × R × RG) (small imbalance, equal arms)

Key Formulas Summary

  • Rx = Rs × Rb / Ra
  • Equal-arm bridge (Ra = Rb)
  • Rx = Rs
  • IG = E × ΔR / (4 × R × RG) (small imbalance, equal arms)

The Calibration Procedure

Chapter 5 specifies 7 calibration steps.

Calibration is a comparison: you apply a known reference value to the instrument under test and record what the instrument reads. The difference is the error. You then either: - Adjust the instrument until the error is within the acceptance criterion, or - Record the error as a correction factor to apply to future readings

Locate the acceptance criterion in Chapter 5 or Chapter 7.

Practice Problems

Work these before checking answers.

P4-1. The reference value is 10.000 V. Your instrument reads 10.043 V. (a) What is the error in volts? (b) What is the error as a percentage of the reference value? Show your work.

P4-2. Using the formula for % error: error% = (measured − reference) / reference × 100 Apply it to: reference = 100.0 kHz, measured = 99,985 Hz. (a) Error in Hz. (b) Error in %. (c) Error in ppm.

P4-3. The acceptance criterion in the TM is ±1%. Your measurement gives an error of +0.8%. Does it pass? State your reasoning.

Practice Problem Answers

P4-1. (a) 10.043 − 10.000 = +0.043 V (b) 0.043 / 10.000 × 100 = +0.43%

P4-2. (a) 99,985 − 100,000 = −15 Hz (b) −15 / 100,000 × 100 = −0.015% (c) −15 / 100,000 × 1,000,000 = −150 ppm

P4-3. +0.8% is within ±1%. PASS. State: "error = +0.8%; criterion = ±1%; result = PASS." Always cite the TM section for the criterion.

Self-Check Questions

SC4-1. How many steps does Chapter 5 specify for the calibration procedure?

SC4-2. What reference value(s) does Chapter 5 apply to the instrument under test?

SC4-3. State the calibration acceptance criterion from the TM. Cite the section.

SC4-4. Write the error formula from Appendix A. Include units.

SC4-5. If the instrument reads 2.3% high, is the error positive or negative? What does a positive error indicate?

Answer Key

SC4-1. Count the numbered steps in Chapter 5. (TM Ch. 5)

SC4-2. See Chapter 5 for the reference values applied. These are the known-good inputs used to check the instrument. (TM §5-1)

SC4-3. See TM Chapter 5 or Chapter 7. Copy the criterion exactly with units and section number.

SC4-4. See Appendix A. Write it exactly as shown.

SC4-5. Positive (instrument reads higher than reference). A positive error means the instrument over-reads — it reports a value higher than the true value. (TM App. A)

Checkpoint

Before proceeding, you must be able to: - State the calibration acceptance criterion without looking - Write the error formula from memory - Work a % error and ppm calculation correctly

→ Proceed to Unit 5