Determination of unknown capacitance and inductance using phasor diagrams and AC Circuits
Physics | Magnetism
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Determine an unknown capacitance and its internal resistance using phasor diagrams.
Determine an unknown inductance and its internal resistance using phasor diagrams.
Learn how to draw a phasor diagram of voltage drop for resistors and capacitors in series.
Learn how to draw a phasor diagram of voltage drop for resistors and coil in series.
In this experiment, we perform AC circuit analysis to calculate an unknown capacitance and an unknown inductance in an AC circuit using a phasor diagram. In the first part, which focuses on the capacitance simulation, we connect a resistor and capacitor in series and measure the voltage drop across the whole circuit (Vtotal), the voltage drop across the resistor (VR) and the voltage drop across the capacitor (VCr). Then we draw the phasor diagram for these voltage drops. Using the ratio between voltage drops we can determine the internal resistance of the capacitor and the value of the capacitor. In the second part, which is the inductor simulation, we repeat the similar work again, but we replace the capacitor with an inductor. Then we determine the value of the unknown inductance.
By the end of the measurement of inductance and capacitance experiment, the student should be able to:
Phasor diagrams present a graphical representation, plotted on a coordinate system, of the phase relationship between the voltages and currents within passive components or a whole circuit.
An AC source is an electromotive force whose voltage changes with time. One of its form is a sinusoidal variation:
V=V0 cos(wt)
When this voltage is applied to a circuit containing components like capacitors and inductors, the resultant current varies also according to a sinusoidal relation but with a different phase:
I=I0 cos(wt+φ)
The current and voltage relationship can be represented in two different ways. In the time domain method, the current and voltage are plotted as functions of time as shown in Figure 1.
Figure 1 Current and voltage in time domain
In the phasor diagram method, the current and voltage are represented as vectors and the angle between the vectors represents the phase difference between V and I. Here we distinguish between three different cases according to the value φ as shown in Figure 2.
Figure 2 Phasor diagram
In the measurement of capacitance and inductance experiment, we will study the R-C and R-L circuits.
1- AC circuit with a resistor and a capacitor with an internal resistance:
Figure 3: RC circuit and phasor diagram
2- AC circuit with a resistor and an inductor with an internal resistance:
Figure 4: RL circuit and phasor diagram
From the phasor diagram, we can exploit the ratio between voltage drop VLVR=XLR to calculate the inductance using XL=2πfL -→L=…H
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