Station 2: Current Measurement

Station 2: Current Measurement

Learning objectives: 2, 5

You will find a simple resistor circuit connected to a power supply, a digital multimeter, and an analog ammeter.

Part A: Getting to know the analog ammeter

  1. Look at the analog ammeter. Find the scale you will be using for this measurement. What is the smallest division marked on that scale?
  2. Look carefully at the spacing between divisions. Can you estimate where a measurement falls between two divisions, or does the spacing not allow that? How finely do you think you can read this instrument?
  3. Based on your answers to questions 1 and 2, what is the smallest uncertainty you could honestly claim when reporting a measurement with this ammeter? Write down your reasoning.

The smallest division on an analog instrument is called the least count. The smallest uncertainty you can honestly claim when using an instrument is called the Instrument Limit of Error, or ILE. For analog instruments like the ammeter, the ILE is equal to the least count or some fraction of it — your judgment about how finely you can read the scale determines which.

Part B: Getting to know the digital multimeter

  1. Turn on the digital multimeter and set it to measure current. Look at the display. How many decimal places does it show?
  2. Watch the display as the circuit runs. Does the last digit stay stable or does it fluctuate between values?
  3. If the display is stable, the true value lies somewhere between half a last digit below and half a last digit above what is displayed. For example, if the display reads 1.35 A, the true value lies between 1.345 A and 1.355 A. Based on this, what is the ILE of the multimeter when the display is stable?
  4. If the last digit fluctuates, what does that tell you about the instrument’s uncertainty? How would you determine the ILE in that case?
  5. Compare the ILE of the analog ammeter to the ILE of the digital multimeter. Which instrument is more precise?

For digital instruments, the ILE is typically half the value of the last digit when the display is stable. If the last digit fluctuates, the ILE reflects the range of that fluctuation rather than just half the last digit.

Part C: Making measurements

  1. Measure the current through the circuit using the analog ammeter. Record your measurement in the form (measurement ±ILE) with appropriate units.
  2. Now measure the current using the digital multimeter. Record your measurement in the form (measurement ±ILE) with appropriate units.
  3. Compare your two measurements. Do they agree? Which instrument gives you more confidence in your result, and why?
  4. You are told the resistor at your station has a labeled value and tolerance. Record both. What does the tolerance tell you about the uncertainty in the resistance? What is the actual uncertainty in ohms?
  5. If you wanted to calculate the power dissipated in the resistor using P= I2R, which current measurement would you use and why? What would choosing the less precise instrument cost you in terms of confidence in your result?