Notes on Experiment #6

Yes we are going back to this experiment that we skipped a while ago.

Be sure to print a copy of experiment #6 and bring it with you to your lab session. There will not be any copies available in the lab.

We will do experiment #6 AS IS. Follow the instructions as given.

Analog Meters

When attaching a meter to a circuit to make a measurement we would hope that the presence of the meter does not cause voltage and current values in the circuit to change. Analog meters, in order to operate, generally borrow energy from the circuit to which they are attached. This is called "loading the circuit." If the meter uses a very small amount of energy and does not cause voltages or currents to change then we say the meter is a "light load." If the meter draws a great deal of energy and current and voltage values in the circuit change dramatically then then meter is "loading down the circuit" or is "a heavy load."

The Simpson multi-meter is an analog meter and will load a circuit when making a measurement. The DMM is almost an "ideal meter" and as such will be an extremely light load on a circuit. (There are cases when the DMM could load down a circuit however.) We will be using the DMM to observe the loading effect of the Simpson meter on a circuit.

Current Meters

All current meters can be modeled as a resistor R_m. An ideal current meter has R_m=0. A practical current meter has R_m equal to "a very small resistance." The circuit in Figure_1 has a current meter in series with a voltage source and a resistor. The current in the circuit without the meter is

I = V_S /R

If the meter is "in circuit" then the current becomes

I = V_S /(R + R_m )

which is clearly a lower value than the original current. You will notice that this new current will actually be the current that the meter displays!

Voltage Meters

All voltage meters can be modeled as a resistor R_m. An ideal voltage meter has R_m=infinite resistance. A practical voltage meter has R_m equal to "a very large resistance." The circuit in Figure_2 has a voltage meter in parallel with a resistor. The voltage V₂ in the circuit without the meter is (by voltage division)

V₂ = [R₂ /(R₂ + R₁ )] * V_S

If the meter is "in circuit" then the voltage becomes

V₂ = [{R₂ || (R_m } /({R₂ || (R_m } + R₁ )] * V_S

which is clearly a lower value than the original voltage. You will notice that this new voltage will actually be the voltage that the meter displays!

The internal resistance R_m of the Simpson meter as a current meter is not available. If there is time, see if you can calculate it using your data from part 1 of the experiment.

The internal resistance R_m of the Simpson meter as a voltage meter is 20K X the scale setting. So, if the scale is on the 10 volt setting then

R_m = 20K X 10 = 200K

On the 2.5 volt setting

R_m = 20K X 2.5 = 50K

Note that this is the scale setting used here and not the voltage value measured at this setting.

For your circuit analysis in part 2. Calculate V₁ and V₂ with no meter and then again with the meter attached appropriately. Consult your lab manual for available voltage scales on the Simpson meter. Choose an appropriate scale for each measurement.

Have fun.