Estimating Errors

Measurement changes the thing that is measured

Introduction

Whenever you measure the voltage across a component in a circuit or the current through a component you change the very voltage and current that you are measuring.

Material

• We use the circuit board from the book Square Wheels.
• A battery or two in a battery holder, e.g. 1.5 volt AA batteries.
• A bulb.
• Two identical meters.

Assembly

Connect the battery to the bulb so that the bulb glows.

To Do and Notice

Use one meter to measure the voltage across the bulb.

The leads from the meter are placed across the bulb to measure the voltage across the bulb.

Touch the two leads from the meter to the two leads from the bulb.

Continue to measure the voltage with one meter while using the second meter to measure the voltage at the same time.

A second meter is placed in parallel with the first, notice the change in the reading of the first meter, if any.

Notice the change in the reading of the first meter, if any, when the second meter is added.

The change in the reading of the first meter is an estimate for the amount that the voltage in the circuit changed when you added the first meter.

What's Going On?

A meter has an internal resistance. When you connect the meter to a circuit the meter's resistance is added into the circuit.

A perfect voltmeter would have infinite resistance.

Real voltmeters do not have infinite resistance and so they change the voltage across the measured component when they are used to measure the voltage across the component.

Going Further

You can measure the error produced when you insert a current meter into a circuit to measure current through a component in the same way.

Insert one current meter, note the current it measures.

Then insert a second meter in series with the first. Notice the change in current measured by the first meter. The change in current made by adding the second meter is an estimate of the change in current made when the first meter is added to the circuit.

A perfect current meter has zero resistance, it is a short circuit. Real meters have resistance that is not zero.

Math Root

If the second meter lowered the voltage across a bulb by 1%because its internal resistance was added in parallel into a circuit then we estimate that the addition of the first meter into the circuit also lowered the voltage by 1%.

 Scientific Explorations with Paul Doherty © 2005 19 Sep 2005