EXP. 4: The Meter Loading Effect in Series Resistance Circuits
OBJECTIVES
1. To study the effects of measurement instruments on circuits.
2. To make further application of Ohm's Law, KCL, KVL, and the effect of parallel combinations of resistances.
BACKGROUND & THEORY
The following circuit consisting of a D.C. voltage source and three parallel voltage dividers. Each voltage divider consists of two resistors connected in series. The node voltages in volts are shown in the ovals and branch currents in milliamperes or microamperes are shown in boxes next to arrows that show the direction of flow. These values are the values present in the circuit without a meter connected to measure them. Remember that node voltages are measured from the reference node to the node in question and the branch or element voltage is the difference between the node voltages at each end of the element.
The voltage V1 across R1 and V2 across R2 for any of these voltage dividers can be calculated using voltage division.
The Currents in each branch can be calculated using Ohm's Law and the series combination of the resistors in each branch.
Now add a voltmeter (of internal resistance Rm) to the above circuit and obtain Circuit 2. With the meter connected as shown, there is now a second path for the current to flow through part of the third voltage divider. The total current through R2C has increased which increases the voltage across R2C. This in turn has caused the voltage across R1C to decrease and therefore the current through R1C has decreased.
Circuit 2
If the meter is placed across R2C then the voltage across R1C will increase and the voltage across R2C will decrease as shown in the circuit below.
Circuit 3
This can be explained by determining the equivalent resistance formed by the meter in parallel with the circuit resistance. In the first case REq. 1 is formed when the meter is in parallel with R1. In the second case REq. 2 is formed when the meter is in parallel with R2.
Using these equivalent resistances and recalculating the voltage division the new values of the two voltages as seen by the meter can be calculated. V'1 is the voltage across R1 when the meter is across R1. V'2 is the voltage across R2 when the meter is across R2.
Remember when you put a resistor in parallel with another resistor, the equivalent resistance is less than the smaller of the two resistances. Therefore when the meter resistance is smaller than the circuit resistance, the measured voltage can greatly differ from the voltage that is across the resistor when the meter is not in the circuit. If the meter resistance is much greater than the circuit resistance then the effect is very small. This effect is called the meter loading effect. Check your text book for a discussion of a loaded voltage divider.
When making current measurements the meter is placed in series with the circuit element. there will be a small voltage drop across the meter. This meter voltage drop will cause the voltage across the circuit element to be smaller than it was without the meter in the circuit, therefore the measures current is slightly smaller than the current normally flowing the circuit. This effect will be greater when the meter voltage drop, often called meter burden, is a larger fraction of the total voltage.
EQUIPMENT AND PARTS LIST
Digital Multimeter (DMM)
Analog Multimeter (AMM)
Adjustable D.C. Power Supply
Circuit Bread Board
Resistors: R1 R2
Branch A 1.5 kW, 2.2 kW,
Branch B 18kW, 56 kW,
Branch C 390 kW, 1.2 MW
PROCEDURE 1:
1. Measure and record the resistances of all six resistors.
2. Construct a circuit similar to Circuit 1 using resistors listed above setting, VS, to approximately 10V D.C. Make sure it is not over 10 volts when measured on the analog meter. Use each meter to measure, VS, and record these measurements. Use the 10 V scale on the analog multimeter and the 40 V or the 4 Vscale on the digital multimeter. When reading the analog meter be sure to position your eye so that the reflection of the pointer is hidden below the pointer. This will eliminate the parallax error caused by viewing the scale behind the pointer from any direction except exactly 90°.
3. Measure V1A' and V2A' using the digital multimeter on 40V scale.
4. Repeat 3. above using the analog multimeter on 10V scale.
5. Repeat 3 & 4 using resistors from Set B.
6. Repeat 3 & 4 using resistors from Set C.
7. Use your DMM to measure the input impedance of the AMM on each of the 4 lowest ranges. Then join with another group so that you have two DMMs and use one DMM to measure the input impedance of the other DMM. Check the DMM impedance on several different voltage ranges.
PROCEDURE 2:
Place a 3.3 kW resistor in series with the 6 V output of the power supply. Set the output for 1 V. Set the DMM for 5 digit display by pressing and holding the small white button for 5 seconds. Measure the current using both the 40 mA range and the 4000 mA range. Repeat the measurements with a 33 kW resistor and a 10 V source voltage. measure both resistor values.
COMPARISONS AND QUESTIONS
1. Referring to Circuit 1 and using voltage division, calculate
V1 and V2, using the measured value of VS
for each meter, and using the measured values of resistances.
These calculations will have to be done separately for each meter since
it is unlikely that the measured value of VS will be the same
for both meters. Perform these calculations for each of the three
sets of resistors, working to at least three decimal places. Then repeat
the calculations including the meter loading effect and find V1'
and
V2' for each to the two meters.
*Be sure to make calculations using the measured values of the resistors and
the measured values of VS with each meter.
Make a tabulation of voltages showing calculated values (V1
and V2, without meter loading), (V1' and
V2' with meter loading), and the measured values V1'
and V2' .Calculate the percent (%) total error (measured value
- value calculated without meter loading as a % of the calculated value),
meter loading error (MLE - this is the difference in the two calculated
values with and without the meter). Finally compare the measured
voltage with the predicted measurement with loading and show this difference
as a % of the nonloaded value. This last difference includes all
the measurement errors except the meter loading effect.
Calculate percent meter loading error per the following.
% MLE = 100*(Voltage with meter - Voltage without meter)/Voltage without meter
Make the above tabulation for each set of resistors and for both DMM and AMM. ( suggested format for your tabulation).
2. From your tabulation in 1., which meter introduces the least amount of meter loading error?
3. Does the amount of error change? What conditions cause the meter loading error to change?
4. Looking at the specification sheets for the DMM and AMM:
a. What is the internal resistance of each meter?
b. What is the accuracy of the voltage readings for each meter?
5. What are some of the sources of error other than the meter loading effect? How important is each one in this experiment?
6. Compare the meter loading error to the other errors for each meter.
7. When a current meter is placed in series with a resistor to measure its current there is a low internal meter resistance in series with the circuit resistance. This will increase the total resistance in the circuit and therefore decrease the actual current that flows when the meter is in the circuit. The resistance of the current meter changes as you chance ranges. The smaller the full scale reading the larger the resistance. On the BK Precision model 2880A digital multimeter the impedance goes from 0.01 Ohms plus any resistance in the connections on the 10 ampere range to 100 Ohms on the 400 µA range. For the 4mA(4000ľA) range it is 100 Ohms and for the 40 mA range it is 1 Ohms. Using your data from Procedure 2 calculate the error caused by the meter resistance and compare the results with your data. Remember that when measuring current the meter is in series with the circuit element not in parallel. Which of your measurements would be more accurate according to this calculation? Include the effects of the basic meter tolerance and digitizing errors.
CONCLUSIONS
Based on the results of the experiment.
Last Updated 01/28/2008