Table of Contents

List of Figures

Figure 1: RL circuit

Figure 2: RC circuit

Figure 3: RLC resonance series circuit

Figure 4: RLC resonance parallel circuit

Exercise 1: Single-Phase RL and RC Circuit in Steady-State

Objective

This exercise aims to highlight the relationships between voltage and current in the case of a passive load consisting of inductive and capacitive elements under single-phase alternating voltage in steady-state conditions.

Part 1: Single-Phase RL Circuit in Steady-State

In the first part, the circuit to observe consists of a series combination of a resistor and an inductance.

Preparatory Activities

To create the requested circuit and better understand the fundamentals, theoretical exercises are requested. The values of the circuit elements are as follows:

• Voltage source:

  

• Source frequency:

  

• 

• 

1. Calculate the instantaneous value of the current

   
   and display the obtained function on the virtual laboratory’s oscilloscope.

2. Same as question 1 but with a source frequency of

   
   . Visualize the current obtained on the virtual laboratory’s oscilloscope.

3. Calculate the value of the resistance so that the phase difference φ between the voltage

   
   and the current
   
   is 45° for a source frequency of
   . Also, visualize the current obtained on the virtual laboratory’s oscilloscope.

Setup Initialization

When the virtual laboratory is launched, the initial parameters in the “Network and Transformer” tab under “Fundamental” and “Harmonic” are set as follows:

a) Set the frequency to 50 Hz.

b) Choose the network as a single-phase network with a phase A voltage of 230 V (since it’s a single-phase network, the phases are set as unbalanced) and no phase shift.

c) Set the transformer in short-circuit mode because it’s not being used.

d) The circuit breaker is not being used; the “Without protection” button is activated.

e) Under the “Harmonic” tab, no harmonics are added. The “A” button is deactivated.

f) Under the “Passive load” tab, choose the configuration “A1 + B1//C1.”

Question 1

In the first question, you are asked to calculate the instantaneous value of the current

and visualize the obtained function on the virtual laboratory’s oscilloscope.

1- The Setup

The requested setup can be performed under the “Passive load” tab as follows:

a) Set impedance Z_1_Series to non-balanced mode (as it’s a single-phase circuit) and choose component A as an RL impedance with values R=20 Ohms and L=100 mH. Components B and C are short-circuited.

b) The other three impedances are balanced circuits with component A short-circuited; they are not used.

2- Take Measurements

Once the setup is completed, the remaining steps are as follows:

a) In the “Network and Transformer” tab, activate the “Power On” button.

b) Open the “Measurements and Calculations” tab and select “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, observe phase A.

c) Observe the signals using the measurements in the “Oscilloscope” tab.

Question 2

For question 2, it’s the same process, but with a source frequency of

. Visualize the current obtained on the virtual laboratory’s oscilloscope.

In this exercise, the setup from the previous exercise remains the same, but the frequency of phase A is changed to 100Hz. Take the same measurements as in question 1 and compare them.

Question 3

For question 3, you are asked to calculate the value of the resistance so that the phase difference φ between the voltage

and the current

is 45° for a source frequency of

. Then, visualize the current obtained on the virtual laboratory’s oscilloscope.

1- The Setup

The requested setup can be performed under the “Passive load” tab as follows:

a) Set impedance Z_1_Series to non-balanced mode and choose component A as an RL impedance with the value L=100mH and the value of R as calculated. Components B and C are short-circuited.

b) The other three impedances are balanced circuits with component A short-circuited.

2- Take Measurements

Once the setup is complete, it remains to take the measurements:

a) In the “Network and Transformer” tab, activate the “Power On” button.

b) Open the “Measurements and Calculations” tab and choose “Rés U” for measurement 1 and “Rés Z_1 I” for measurement 2. For both measurements, phase A is observed.

c) Observe the signals using the measurements in the “Oscilloscope” tab, and verify the requested phase difference in the exercise.

Part 2: Single-Phase RC Circuit in Steady-State

In the second part, the circuit to observe consists of a circuit composed of a resistance R2 in parallel with a capacitor C. This element is in series with a resistance R1.

Preparatory Activities

To create the required circuit and better understand the fundamentals, theoretical exercises are requested. The values of the circuit elements are as follows:

• Voltage source:

• Source frequency:

1. Calculate the current

   at time
   = 8 ms and the current I. Visualize the current
   on the oscilloscope of the virtual laboratory. The circuit is in a steady-state.

Setup Initialization

When the virtual laboratory is launched, the initial settings in the “Network and Transformer” tab under “Fundamental” and “Harmonic” should be adjusted as follows:

a) Set the frequency to 50 Hz.

b) Choose the network as a single-phase network with phase A voltage of 230 V and no phase shift.

c) Set the transformer to short-circuit mode as it is not used.

d) The circuit breaker is not used; the “Without protection” button is enabled.