Introduction:
This is the ninth experiment in which we will be doing a few experiments that involve inductors and capacitors in order to gain a deeper insight into these elements. We will carry out a few experiments that concern open-close switch circuits and the first order circuit. We shall determine the R(internal) value for the inductors as well as the capacitors in the first order circuit.
Theory:
A capacitor is an element with two terminals that models a device that contains two plates capable of conduction, with the plates being separated by a material that is a non-conductor.
The relationship between voltage and current for a capacitor is-
Vc(t)=V. + 1/C integral from 0 to t of ic(t)dt
An inductor is an element comprising of two terminals, and consists of a winding with N number of turns. Inductance is introduced in an electrical circuit via the winding.
The relationship between voltage and current for an inductor is-
iL(t)= 1/L integral from – infinity to t of Vl (t) dt
Procedure and Results:
The circuit depicted in Figure 1.1. was created and the R(internal) value calculated. The value of Rint = 48.15Ω.
Figure (1.1) Schematic circuit I with capacitor
The circuit as shown in Figure 1.2 was created, and the time constant and the voltage present across the capacitor calculated.
Figure (1.2): Schematic for circuit II
Figure(1.3) Sketch of the waveform in which the capacitor is discharging
Results:
When R=6.8kΩ
Figure(1.4) Schematic for circuit II with 6.8kΩ
Figure(1.5) Sketch of the waveform in which the capacitor is discharging
The circuit as shown in Figure 1.6 was created, and time constant and voltage present across the inductor calculated.
Figure( 1.6) Circuit of the inductor
Figure(1.7) Sketch of the voltage
Results:
The number of the Unknown Inductor #3
Figure(1.8) The circuit of the unknown inductor
Results:
Rdc=0.27Ω
Time constant= L/R+Rint
L=time constant*(R+Rint)
L=11*10^-4*730.63
L=0.803H
Discussion
When calculating, converting back and forth between the rectangular and polar forms was essential. When performing the addition or subtraction of phasors, it was necessary to first convert them into the rectangular form. When performing the division and multiplication of phasors, it was necessary to use the polar form. Graphs of the phasor currents and voltages, and impedances were plotted in the rectangular form. The accuracy of the graphs plotted was verified using the polar form angle. The graphs also enabled visual verification of V1+V2=Vs.
Conclusion:
After conducting the experiment, we could build a circuit consisting of an inductor and a capacitor. The experiment helped us to gain a deeper understanding of the relationship between the current and voltage of inductors and capacitors. R-L and R-C circuits were built and the voltage value was determined using different resistors. Through this lab, students learnt to calculate the impedances of capacitors and inductors in the circuits of the RLC series. In addition, they learnt to calculate the currents and voltages of phasors.
