.
Purpose
The purpose of this exercise is to develop proficiency in the use of the digital multimeter in the
context of verifying Kirchhoff's Voltage and Current Laws (KVL and KCL).
Equipment Required
• DC power supply
• Digital Multimeter
2. Using the Multimeter as a Voltmeter
A voltmeter is a device for measuring voltage. It measures the voltage drop from the red to the
black probes. The voltmeter is placed in parallel with the circuit element whose voltage is to be
measured. Recall that two elements are in parallel when they share the same pair of nodes and
hence share the same voltage. Consider the voltage divider circuit shown in Figure 1 in which
the voltage across R2 is to be measured. If the presence of the voltmeter does not affect the
voltage it is intending to measure, the meter must draw no current. That is, it must act as an
open circuit. An open circuit may be thought of as an infinite resistance. Hence, an ideal
voltmeter has an infinite resistance. You measured the internal resistance of the voltmeter in
Experiment 2 and found the value to be on the order of MW which is large, but certainly not
infinite.
Figure 1 Voltage Divider Circuit
First consider the circuit with the voltmeter not present. In this case the voltage vx can be
expressed in terms of the source voltage vs and the resistors R1 and R2 by
With the voltmeter present, its resistance alters the voltage division equation which becomes
where RM is the resistance of the voltmeter. You will not be able to see how this equation was
obtained at first examination. Let the voltmeter in Figure 1 be represented by a resistance RM.
Use resistance reduction and voltage division to obtain an expression for vx in terms of vs. Then,
clear the fractions in the numerator and denominator. Be sure to show your derivation in your
lab report. Recall that an ideal voltmeter has infinite resistance. Letting the value of RM in
Equation 2 be infinite should result in Equation 1. Derive equation 1 from Equation 2 by taking
the limit as RM ® ¥. L'Hospital's Rule may be helpful.
You will now build the voltage divider circuit using the DC power supply as the voltage source
2.1 Voltage Divider with Moderate-Valued Resistors
1. Obtain two 1 kW resistors from the parts bin. Designate one of the resistors as R1 and the
other as R2.
2. Measure the resistor values using the multimeter as an ohmmeter. Be sure to keep track of
which resistor corresponds to which value measured!
3. Build the circuit in Figure 2 using the 1 kW resistors for R1 and R2.
4. Set the power supply to 5V. Use the voltmeter, not the front panel display of the power
supply to ensure the proper setting. Important Note: You built the circuit before you set the
power supply voltage to 5V. If the current limiter is set to a value lower than than the current
demanded by the circuit, the constant current (cc) indicator will light up and the voltage
control knob will no longer adjust the output voltage. If this happens, simply increase the
current limiter until you are able to achieve 5V in the constant voltage (cv) mode.
5. Using the voltmeter, measure the voltage across resistor R1, and then across resistor R2.
Record these values, as always, and verify Kirchhoff's Voltage Law KVL.
6. Comment on the accuracy of measurements made considering the internal resistance of the
voltmeter.
7. Create a table presenting theoretical and measured voltages along with percent error.
Consider whether your theoretical values for the voltages across R1 and R2 should include
the effect of RM. Important Note: When you are calculating percent error, you should avoid
cases in which the theoretical value is zero since the percent error is meaningless. To
calculate percent error between theoretical and experimental verification of KVL, use the
source voltage as the reference. For example, in the measurements made in this section, the
theoretical value (and measured value!) for the voltage across the supply is 5V. The
measured value is the same as the theoretical value because you used the voltmeter to set the
power supply voltage to 5V. To obtain the KVL measured voltage, add the voltage across R1
to the voltage across R2. Compare with 5V.
2.2 Voltage Divider with Large-Valued Resistors
1) Obtain two 10 MW resistors from the parts bin. Designate one of the resistors as R1 and the
other as R2.
2) Measure the resistor values using the multimeter as an ohmmeter. Be sure to keep track of
which resistor corresponds to which value measured!
3) Build the circuit in Figure 2 using the 10 MW resistors for R1 and R2.
4) Set the power supply to 5V.
5) Using the voltmeter, measure the voltage across resistor R1, and then across resistor R2.
Record these values, as always, and verify Kirchhoff's Voltage Law KVL.
6) Comment on the accuracy of the voltage measurements made (consider the internal
resistance of the voltmeter).
7) Create a table presenting theoretical and measured voltages along with percent error.
Consider whether your theoretical values for the voltages across R1 and R2 should include
the effect of RM.
3. Using the Multimeter as an Ammeter
An ammeter is a device for measuring current. It measures the current flowing from the red to
the black probes within the meter. The ammeter is placed in series with the circuit element
whose current is to be measured. Recall that two elements are in series when they share in the
same branch and hence share the same current. Consider the current divider circuit
The purpose of this exercise is to develop proficiency in the use of the digital multimeter in the
context of verifying Kirchhoff's Voltage and Current Laws (KVL and KCL).
Equipment Required
• DC power supply
• Digital Multimeter
2. Using the Multimeter as a Voltmeter
A voltmeter is a device for measuring voltage. It measures the voltage drop from the red to the
black probes. The voltmeter is placed in parallel with the circuit element whose voltage is to be
measured. Recall that two elements are in parallel when they share the same pair of nodes and
hence share the same voltage. Consider the voltage divider circuit shown in Figure 1 in which
the voltage across R2 is to be measured. If the presence of the voltmeter does not affect the
voltage it is intending to measure, the meter must draw no current. That is, it must act as an
open circuit. An open circuit may be thought of as an infinite resistance. Hence, an ideal
voltmeter has an infinite resistance. You measured the internal resistance of the voltmeter in
Experiment 2 and found the value to be on the order of MW which is large, but certainly not
infinite.
Figure 1 Voltage Divider Circuit
First consider the circuit with the voltmeter not present. In this case the voltage vx can be
expressed in terms of the source voltage vs and the resistors R1 and R2 by
With the voltmeter present, its resistance alters the voltage division equation which becomes
where RM is the resistance of the voltmeter. You will not be able to see how this equation was
obtained at first examination. Let the voltmeter in Figure 1 be represented by a resistance RM.
Use resistance reduction and voltage division to obtain an expression for vx in terms of vs. Then,
clear the fractions in the numerator and denominator. Be sure to show your derivation in your
lab report. Recall that an ideal voltmeter has infinite resistance. Letting the value of RM in
Equation 2 be infinite should result in Equation 1. Derive equation 1 from Equation 2 by taking
the limit as RM ® ¥. L'Hospital's Rule may be helpful.
You will now build the voltage divider circuit using the DC power supply as the voltage source
2.1 Voltage Divider with Moderate-Valued Resistors
1. Obtain two 1 kW resistors from the parts bin. Designate one of the resistors as R1 and the
other as R2.
2. Measure the resistor values using the multimeter as an ohmmeter. Be sure to keep track of
which resistor corresponds to which value measured!
3. Build the circuit in Figure 2 using the 1 kW resistors for R1 and R2.
4. Set the power supply to 5V. Use the voltmeter, not the front panel display of the power
supply to ensure the proper setting. Important Note: You built the circuit before you set the
power supply voltage to 5V. If the current limiter is set to a value lower than than the current
demanded by the circuit, the constant current (cc) indicator will light up and the voltage
control knob will no longer adjust the output voltage. If this happens, simply increase the
current limiter until you are able to achieve 5V in the constant voltage (cv) mode.
5. Using the voltmeter, measure the voltage across resistor R1, and then across resistor R2.
Record these values, as always, and verify Kirchhoff's Voltage Law KVL.
6. Comment on the accuracy of measurements made considering the internal resistance of the
voltmeter.
7. Create a table presenting theoretical and measured voltages along with percent error.
Consider whether your theoretical values for the voltages across R1 and R2 should include
the effect of RM. Important Note: When you are calculating percent error, you should avoid
cases in which the theoretical value is zero since the percent error is meaningless. To
calculate percent error between theoretical and experimental verification of KVL, use the
source voltage as the reference. For example, in the measurements made in this section, the
theoretical value (and measured value!) for the voltage across the supply is 5V. The
measured value is the same as the theoretical value because you used the voltmeter to set the
power supply voltage to 5V. To obtain the KVL measured voltage, add the voltage across R1
to the voltage across R2. Compare with 5V.
2.2 Voltage Divider with Large-Valued Resistors
1) Obtain two 10 MW resistors from the parts bin. Designate one of the resistors as R1 and the
other as R2.
2) Measure the resistor values using the multimeter as an ohmmeter. Be sure to keep track of
which resistor corresponds to which value measured!
3) Build the circuit in Figure 2 using the 10 MW resistors for R1 and R2.
4) Set the power supply to 5V.
5) Using the voltmeter, measure the voltage across resistor R1, and then across resistor R2.
Record these values, as always, and verify Kirchhoff's Voltage Law KVL.
6) Comment on the accuracy of the voltage measurements made (consider the internal
resistance of the voltmeter).
7) Create a table presenting theoretical and measured voltages along with percent error.
Consider whether your theoretical values for the voltages across R1 and R2 should include
the effect of RM.
3. Using the Multimeter as an Ammeter
An ammeter is a device for measuring current. It measures the current flowing from the red to
the black probes within the meter. The ammeter is placed in series with the circuit element
whose current is to be measured. Recall that two elements are in series when they share in the
same branch and hence share the same current. Consider the current divider circuit