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Objectives: 1. To investigate the characteristics of the series resonant circuit 2. To determine the resonance curve Apparatus : Digital Multimeter (DMM): Dual Beams Oscilloscope: Function Generator, breadboard Components: Capacitor decade box: Resistor decade box: Inductor decade box PART A: Background of RLC Series Resonant Circuit Consider a RLC series circuit shown in Figure 1 and the relevant phasor diagram shown in Figure 2. In the phasor diagram it is assumed that the capacitive reactance is less than the inductive reactance. theee my Figure 1 Figure 2 Ve-Ve The magnitude of the impedance of the circuit in complex number form is equal to : z = = = R + Xc + Xc Now consider the circuit in Figure 1 in which the supply operates with a varying frequency. When the frequency is zero, i.e. corresponding to a d.c. supply, X = 2n fL=0 and XC= =00, 1 2xƒC As the frequency increases, Xy increases, while XC decreases inversely. At a frequency fs, XL-XC. resonance is said to have occurred. fg is called the resonant frequency and is equal to: It can be found from the phasor diagram that for the condition of resonance, the reactance of the inductor and the capacitor being equal, the supply voltage and the supply current are in phase and the circuit impedance is equal to the resistance R. The resonant current is dependent on the resistance and the V value of current given by I- R At resonance, the ratio of voltage across the capacitor or inductor to the supply voltage is called the wo, L Q factor of the resonant circuit. Q- 1 R 00,CR
900 750m 600 PART B: To find the resonant frequency of Series RLC Circuit At L- 450m 300 150 (internal resistance = Function Generator Figure 3 IK rele Vin=2Vpp connected CRO CHI Freq (Hz) Ik 2k VK (Volt- Peak) State the resonant frequency equation: f= Calculate the resonant frequency, f. 1.1 Connect the circuit shown in Figure 3 and connect the CRO Ch2 across the Va (Ground probe of the CRO must connect to the ground clip of the function generator) 2k µH 2) measured by DMM 3k C=__UE 1.2(a) Vary the function generator frequency and observe the waveforms of Vin and VR- (Note: Throughout the experiment, Vin must be kept constant at 2 volt peak-peak when changing frequency, and adjust if require) 1.2(b) Record the peak values of F' (observe by CRO) at different frequency and fill in the table: Det M 30k 3k 4k śk 6k 7k 9k lok 160m 300m 500m 140m 960m 7bom 660m 580m 440m 420m 1.3 Plot the frequency response curve: VR (Y-axis) against frequency (X-axis) with suitable scale. R= 4k 2 www 1 5k 6k 1k 50 8k 8k 9k lok
1.4 From the frequency response curve, determined the maximum value of Ve on the graph and hence find resonance frequency, f, of the circuit. 1.5(a) Write down the formula and calculate the inductive reactance (XL) and capacitive reactance (X) when resonance occurs on the circuit. X₁: Xc (12) 1.5(b) Is the circuit impedance equals to the resistance of the circuit when resonance occurs? (Yes/No?) Explain: 1.5(c) State the relationship of the circuit current and impedance when resonance occurs in a RLC series circuit: /is (Max /Min) at Impedance is (Max /Min) when resonance. 1.6 Calculate the Q-factor of the circuit where Q- QI Q R
PART C: DISCUSSIONS 1. Compare the experimental results with the theoretical results of the resonance frequency. 2. Comment on the difference between the experimental results with the theoretical results. - END -