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parallel rlc problems capacitive inductance reactive capacitance
Typology: Lab Reports
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Resistance and impedance both represent opposition to the flow of the alternating current. Both are measured in terms of the same unit, the ohm. To determine the magnitude of the total impedance, get the sum of the impedance of each of the elements in series. As long as all the necessary calculations are carried out by vector algebra, use the two relationships studied earlier under DC circuits. The total impedance may not always increase with the addition of another element in series. Capacitive reactance could cancel out inductive reactance and vice versa. An extreme case would have the capacitive reactance completely cancelling out the inductive reactance. This results in resonance high voltages and current could result. To know the concept of a series RLC circuit is to study basic knowledge concerning it, starting with the RLC circuits itself. In an RLC circuit; the resistor (R), inductor (L), and capacitor (C) are connected to the supply (voltage). This circuit was named after its components. These elements are passive in nature (consume energy rather than producing it) and have linear relationship (between voltage and current). RLC circuits have many applications as oscillator circuits. It can be used for tuning and selecting narrow range of frequencies (radio waves) and sometimes referred to as a second-order circuit as any current or voltage in the circuit can be described by a second order differential equation in a circuit analysis. The RLC circuit exhibits the property of resonance in the same way as LC (inductor and capacitor) circuit exhibits, but in this circuit the oscillation dies out quickly as compared to LC circuit due to the presence of resistor in the circuit. The three circuit components (elements); resistor, inductor and capacitor, can be combined in a number of different topologies (can be connected across the voltage in series and in parallel), though there are other various arrangements possible.
Figure 2A Figure 2B
Figure 2C Figure 2D c. Measure the voltage eT , eR , eL and eC. To measure the voltage eT refer to figure 3a. Record the data at table 2. Repeat the step for the lamp, inductor and capacitor. Refer for the figure 3b, 3c and 3d. Figure 3A
e. Compute the magnitude and phase angle of the impedance using the equation Zโ = R โ jXc + jXl, where Xl = 2๐๐๐ฟ and Xc = 1/2๐๐๐ถ. Use the 4 uF for the value of and 2.5372 H inductor for the value of L. f. Compute the percent difference between the measure and the computed value of the impedance.
b. Give possible reasons for any discrepancies.
B. Circuit Design a. Design a series RLC circuit which is connected to 220 V , 50 cycles, having a 100W, capacitor C and inductor L. The total impedance is 609.8121 ohms and the capacitive reactance is 530.5165 ohms. Find the value of R, L and C
Given: V= 220 V ZT= 609.8121 ฮฉ P= 100 W XC= 530.5165 ฮฉ f= 50 Hz Required: Resistance (R) Inductance (L) Capacitance (C) Solution: Computing for the value of Resistance (R):
C. Problems a. Under what conditions could the total impedance of two impedances in series be less than that of either one by itself?
most only one value and four unknowns. To get all of these there is a finite number to choose from and it will take a long time to determine the total impedance. We canโt actually get the total impedance given the magnitude only. VI. CONCLUSION Series RLC circuit is simply a circuit in series of the three elementary components of electronics which are the resistor, inductor, and capacitor. The impedance of the circuit is the total opposition to the flow of current. The impedance of a resistor is a real number and the impedances of the inductor and capacitor are pure imaginary numbers, the total impedance of the circuit is a sum of these three impedances and is considered as a complex number. Resonance happens when the impedance of a capacitor and inductor are equal and cancel out. So only real resistance is there. The energy stored in the capacitor and inductor oscillates between them. The source voltage represented by VS is the phasor sum made up of three components namely VR, VL and VC. The current is common to all three components and is used as the horizontal reference when constructing a voltage triangle. The voltage drop across the resistive element is equal to IR, the voltage across the two reactive elements is IX = IXL โ IXC while the source voltage is equal to I*Z. The angle between VS and I will be the phase angle. Take note that if voltage leads the current then the circuit is inductive. Otherwise, if the current leads voltage then the circuit is considered to be capacitive. As evidenced in Table 1 & 2, the workbench and computational values of voltage and current of the Series RLC circuit showed approximately the same results but still different due to minimal discrepancies. It is because multisim assumes some small resistances while human computation takes estimations.
