Exercise 2 – Voltages and currents measurements
1.
Aim of the exercise
The aim of the exercise is to familiarize students with the methods of measuring voltages and
currents in the actual electric circuits. Another aim is to getting the ability of measurement
uncertainty evaluation and measurement equipment familiarization.
Main topics
 Direct voltage and current measurements
 Indirect current measurements
 Measurements of EMF of actual voltage sources, acquisition errors estimation,
internal source resistance estimation
 Compensation method for EMF measurement
2.
Gained skills
 the ability to measure voltages and currents
 the ability to determine the current value with the indirect method,
 the ability to measure the EMF of the actual source and determine its internal
resistance
 the ability to measure the EMF with the compensation method,
3.
Instrumentation
Figure 1. Measurement box U01
4.
Measurements and tasks
Task 1 – Direct and indirect voltage and current measurements

With the use of the module U01 (Fig. 1) connect the measurement circuit from Figure 2.
The power supply should be connected to “WE” connectors. The output voltage, current
limit and the resistance to adjust on the decade resistor will be provided by the
supervisor. For the voltage measurement use the 34450A multimeter and for the current
measurement U1252B handheld one.
I
+
+
A
–
+
V
E
–
U
Rx
–
Figure 2 Schematic diagram for simple voltage and current measurement


After measuring the current with the meter, calculate its value by applying the Ohm’s law
(Hence, you measure it now also indirectly).
Compare the values and the errors of both measurements.
Task 2. Voltage measurement on a real voltage source. Estimating internal resistance of the
source.



Use LM-3 voltmeter (class 0.5) and 34450A multimeter (10 MΩ internal resistance) to
measure the voltage on Źr. 1, Źr. 2 and Źr 3 sources.
What is the reason of the discrepancy in the meters’ readings for “Źr. 1”, “Źr. 2” and
“Źr. 3”?
Can you quickly estimate the internal resistance of “Źr. 2”? Have you got idea how you
can calculate it quite precisely?
NOTE: Taking measurements with LM-3 meter, select the lowest possible range for “Źr. 1”, and
DO NOT change it during subsequent measurements.
Task 3. Compensation method

Connect the circuit according to Figure 3. Use the compensation method to measure the
voltage at “Źr. 3”.

Estimate the relative error of the method.
!
What can you say about the method’s advantage?
Rx
„0”
V
Ex
Uref
Eref
Figure 3. Schematic diagram for voltage measurement with usage of compensation method.
𝛿𝑔 𝑈 = 𝛿𝑔 𝑈𝑟𝑒𝑓 +
∆𝑈
∙ 100%
𝑈𝑟𝑒𝑓
where: ΔU – is the lowest voltage possible to read on the zero indicator.
5.
Control questions
1. What is the acquisition error?
2. Define the class index of the meter.
3. Is the relative error of a voltmeter of 0.5 class index always equal to 0.5 %? Justify the
answer.
4. What is the connection configuration of the ammeter and what of the voltmeter to the
electric circuit?
5. Draw the scheme for the voltage measurement with the compensation method. What
are the requirements for the voltmeters to obtain the error as small as possible?
6. What is the internal resistance influence on the measurement results for:
-
An ideal voltage source
-
A real voltage source
7. What will be the voltmeter’s indication if it has the internal resistance of 10 kΩ when
measuring voltage on the real source with EMF of 10V and internal resistance of 10 kΩ?
8. What value should be internal resistances of ideal voltmeter and of ideal ammeter?
9. The voltage was measured on the real voltage source of the EMF = 5V. The result was
2.5 V. What is the internal source resistance if the voltmeter internal resistance is
100 kΩ.
10. The current was measured with the use of the ammeter. The result was I = 10 mA at
the range of 50 mA. Calculate the relative error if the formula for the ammeter limiting
error is given by formula:
𝛿𝑔 𝐼 = 0.05% + 0.02% ∙
𝐼𝐹𝑆
𝐼
11. The current was measured indirectly by the measurement of the voltage drop on the
R = 10 kΩ resistor. The result of the voltage measurement was U = 10V. Calculate the
current value and the relative error of its measurement if the error of the voltage
measurement is given by formula:
𝑈𝐹𝑆
𝛿𝑔 𝑈 = 0.05% + 0.01% ∙
𝑈
12. The EFM was measured with the use of the compensation method. The result was
U = 10 V at the range of 30 V. Calculate the relative error if the voltage measurement
was performed with the meter for which the relative error is given by a formula:
𝛿𝑔 𝑈 = 0.05% + 0.01% ∙
𝑈𝐹𝑆
𝑈
The zero indicator has the resolution of 0.01 mV.
13. The EFM was measured with the use of the compensation method. The result was
U =5 V at the range of 10 V. What should be the resolution of the balance indicator for
the insensitivity error to be 10 times smaller than the relative error of the voltage
measurement by the meter given by the formula:
𝛿𝑔 𝑈 = 0.05% + 0.01% ∙
𝑈𝐹𝑆
𝑈