Introduction
This laboratory experiment is about the simulation and testing of sinusoidal circuits in steady state and the analysis of the currents and voltages in the circuits. The circuits being analyzed are (1) an RC circuit and (2) an RLC circuit. The steady-state voltages and currents are evaluated if they comply with KVL and KCL. Additionally, in the RLC circuit, the power dissipated on the resistor and the total power delivered by the source are compared and analyzed.
Purpose of the Experiment
The purpose of this experiment is to measure the steady-state currents and voltages in the RC and RLC circuits (by experimentation and by simulation), and analyze them through phasor analysis whether they follow theory (KVL and KCL) or not. Moreover, the power dissipated on the resistor on steady-state is compared with the total power delivered by the source.
Equipment and Components
The equipment and component values are listed below:
Function generator
Oscilloscope
Digital Multimeter
MULTISIM
25 mH Inductor
0.1 µF Capacitor
1 kΩ and 2.4 kΩ Resistors
MULTISIM is the software used for simulation of the two circuits. All the others in the list are used in the experimental setup of this laboratory.
Procedure
PART A
The first part of the laboratory uses the RC circuit of figure 1. The input is a sine voltage with 10 Vp-p, 1 kHz.
Figure 1. Series RC Circuit
The voltages and phase differences across the capacitor and resistor are measured (experimentally and by simulation in MULTISIM). Then, the values are tabulated, including an additional table column of percentage error compared to theoretical values. An AC sweep is simulated with frequencies from 1 Hz to 50 kHz. The phasor representations of the voltages are used to prove KVL in the series circuit.
PART B
The second part of the laboratory uses the RLC circuit of figure 2.
Figure 2. RLC Circuit
The steady state voltages and currents on the components (resistor, inductor, and capacitor) are measured (both experimentally and by simulation in MULTISIM). Then, the values are tabulated, including an additional table column of percentage error compared to theoretical values. Additionally, the total power from the source and the power dissipated on the resistor are computed and compared.
Results and Analysis
The total impedance of the RC circuit is:
Ztotal=2.4k+1j2π1k0.1μ=2.4k-j1.592k Ω
The theoretical voltages are:
vc=5V∠-90° -j1.592k2.4k-j1.592k= 2.76∠-146.45°
vR=5V∠-90° 2.4k2.4k-j1.592k=4.167∠-56.45°
The experimental voltages are all within less than 6% error compared with the theoretical values. The sum of the experimental voltages in phasor is (KVL of circuit):
VS=2.6∠-145.66°+ 4.10∠-57.92°=4.94∠-89.64°
The experimental phasor representation of the voltage source is still very close to the theoretical value (5∠-90° V).
AC sweep of the RC circuit is shown in figure 3.
Figure 3. AC Sweep from 1 Hz to 50 kHz of RC Circuit
The equivalent impedance for the RLC network is:
Ztotal=1k+j2π1k25m||1j2π1k0.1μ=1k+j174.28
The theoretical voltages are:
vC=vL=5V∠-90° j174.281k+j174.28=0.8585∠-9.886
vR=5V∠-90° 1k1k+j174.28=4.9258∠-99.886
The results for PART B are shown in table 2.
The errors obtained in this experiment are very high. In particular, the capacitor phase has an error of 222%. The only low error was obtained on the resistor phase (2%). The phasor addition, it was found that the source voltage is:
VS=0.98∠-31.85°+ 4.30∠-101.88°=4.72∠-90.6°
The phase difference is near, but the magnitude is slightly off from the expected 5V.
The current coming from the source can be computed from the resistor.
IT=vRR=4.301k=4.3 mA
Thus, the average total power delivered by the supply is:
PTotal=V×IT=5V×4.3 mA=21.5 mW
The power dissipated by the resistor is:
PR=IT2R=4.3m21000=18.5 mW
The percentage of power dissipated in the resistor to the total power is:
%Power=18.521.5×100%=86.05%
This value shows that the majority of the power supplied by the source is being dissipated in the resistor. The rest of the power delivered is stored in the capacitor and inductor (only about 14%).
