Names: Farhan Labib Rashid ID- 2112483625, Shohana Akter Shoshi ID- 2121098643, Lubna
Islam ID- 2121233643, Toky Tahmid Efty, ID- 2121103643
Group-11
Lab 3: Series RLC circuits
Experiment 1: Series RLC circuits
Objective
To analyze the relationship between the voltage and phase of
reactive elements and the source in series RC, RL and RLC
circuits.
Apparatus
Components Instruments
• Resistors: 1×1kΩ • 1× Trainer Board
• Capacitors: 1×0.1µF • 1× Audio Generator
• 1× Dual Channel Oscilloscope
Inductor: 1x478mH • Connecting wires and probes
Constructing Circuit(Series RC)
Fig. Series RC circuit
Swapping R and C:
|Vpeak| Delay ΔT θ (Practical)
|Vpeak| θ
(Practical) (Practical) [ΔT x f x 360] % Difference |V| % Difference θ
(Theory) (Theory)
(V) (µS) (º)
VC 11.8 98 35.28
VR 7.46 156 56.16
ΘR= ΔT x f x 360=(124*10-6)(1000)(360)=56.16
0
35.280
ΘC= ΔT x f x 360=(98*10-6)(1000)(360)=
Constructing Circuit (Series RL)
Fig.Series RL circuit
Swapping R and L:
|Vpeak| θ |V |
peak Delay ΔT θ % %
(Theory) (Practical) (Practical) (Practical) Difference Difference
(Theory
(V) (µS) [ΔT x f x |V| θ
360]
(º)
VL 13.2V 50 18
VR 4.4V 200 72
ΘL= ΔT x f x 360
=50*(1/1000)*360=180
ΘR= ΔT x f x 360
=200*(1/1000)*360=720
Constructing Circuit 3 (Series RLC)
Voltage and Current in an AC circuit:
The complex impedance in an AC circuit is represented by Z and expressed in Cartesian form by the
formula:
where the
real part of impedance is the resistance R and the imaginary part is the
reactance X.
Impedance can also be expressed in magnitude and phase form: , where θ is the phase difference
between the voltage and the current. The magnitude of the impedance can be expressed as:
and the phase can be expressed as: .
It follows, then, that since Ohm’s Law is true for AC circuits, the current flow caused by a voltage V can be
given by:
Here, VS is the source voltage, IS the source current and
VR, VL and VC the voltages across the resistor, inductor
and capacitor respectively. The complex voltage across
any of the components can be found using the voltage
divider rule. The phase relations of the voltages
mentioned can be expressed by the phasor diagram in
Figure B.1.2:
Fig.B.1.1: Series RLC circuit
We can see that VL and VC are both 90° out of phase with the
circuit current IS, and and out of phase with the source
voltage respectively. We can also see that the voltage across the
resistor is always in phase with the current through the resistor,
which, in this case, is the source current. θL
θC
Fig.B.1.2:
Phasor Diagram
Fig. Series RLC circuit
|V peak| θ |V peak| Delay ΔT θ (Practical)
(Practical) [ΔT x f x 360] % Difference |V| % Difference θ
(Theory) (Theory) (Practical)
VC 12.7V 400µs 144°
VL 24.1V 100µs 36°
VR 8.03V 150µs 54°
Measuring the peak voltage drop and time delay across the capacitor
with the oscilloscope
Measuring the peak voltage drop and time delay across the
inductor with the oscilloscope.
Measuring the peak voltage drop and time delay across the resistor
with the oscilloscope
FOR VC
FOR VL
FOR VR
Calculations of the table:
ΘC = ΔT x f x 360= (400*10-6)*(1000)*(360) = 1440
ΘL = ΔT x f x 360 = (100*10-6)*(1000)*(360) = 360
ΘR = ΔT x f x 360 = (150*10-6)*(1000)*(360) = 540
Questions:
Q1 Draw the phasor diagrams for the series RC, RL and RLC circuits.
Phasor diagram for RC circuit
VR=7.46V
56.160
VS=14V
35.280
VC=11.8v
Phasor Diagram: RL CIRCUIT
VL=13.2V
180
VS=14V
720
VR=4.4V
Phasor diagram for RLC circuit
VL= 24.1V
ᶱl= 36° Vs= 14.0V
VL-C= 11.4V
ᶱr= 54°
Is
VR= 8.03V
ᶱc= 144°
VC= 12.7V
Explanation of the phasor diagrams:
In the phasor diagram of RC circuit, VR leads from the source by
56.16° whereas, VC lags from the source by 35.28°. Thus, VR
leads VC by 90°. There was a little error in our experiment which
is why we get 91.4° when we add our angle but theoretically its
90°.
In the phasor diagram of RL circuit, VL leads from the source by
18° and VR lags from the source by 72°. Theoretically, VL leads
VR by 90° which is proven by adding the angles we got from the
experiment. We had no errors in the RL circuit as the angle
matches the theoretical angle.
In the phasor diagram of RLC circuit, VL leads from the source by
36°, VR lags from the source by 54° and VC lags from the source
by 144°. Theoretically VL leads VR by 90° and we can prove that
by adding the angles 36° and 54°. Also theoretically, VR leads VC
by 90° which is proved by subtracting 54° from 144°. The
magnitude of VL-C is found out by subtracting the magnitude of
VL from VC.
Discussion:
In this experiment we have analyzed the relationship between the voltage
and the phase angle of reactive elements and the source in series RC, RL
and RLC circuits. First of all, we have built those circuits in Multisim software.
Then we have measured the peak voltage across all the elements using
measure operation and the time difference delta from those circuits using
cursor operation in the Tektronix oscilloscope. After measuring these
variables, we have calculated the phase angle by Θ= ΔT x f x 360. Lastly,
we have drawn the phase diagram to determine which elements are leading
and which elements are lagging to finish the experiment.
