Experiment No. 7: Resonance in Series AC Circuits PDF

Experiment NO. (7) Resonance in Series AC Circuits Objective To investigate the characteristics of a series RLC circuit in the region of resonant frequency Apparatus: -1Dual Beam Oscilloscope -2function Generator -3Resistance Boxes. -4Capacitance Boxes -5inductance Boxes -6digital multi-meter -7coax...

Experiment NO. (7) Resonance in Series AC Circuits Objective To investigate the characteristics of a series RLC circuit in the region of resonant frequency Apparatus: -1Dual Beam Oscilloscope -2function Generator -3Resistance Boxes. -4Capacitance Boxes -5inductance Boxes -6digital multi-meter -7coaxial cables -8connecting wires Theory: A two terminal network, in general, offers complex impedance consisting of resistive and reactive component. lf a sinusoidal voltage is applied to such a network, then the current is out of phase with the applied to such a network, then the current is out of phase with the applied voltage. under special circumstance, the impedance offered by the network is purely resistive. The phenomenon is called resonance and the frequency of the applied signal at which resonance occurs is called the resonance frequency. Series resonance Fig 7.1 illustrates a series connected RLC circuit. A sinusoidal voltage v is applied to the circuit. The circuit said to be resonant when the resultant reactance is zero, i.e. the circuit is purely resistive. The impedance Z of the circuit is given by: Z=R + j𝜔L + 1/( j𝜔C) Where Z & R are in ohms, L in Henrys, C in Farads Fig. 7.1 series RLC circuit Case 1, f< fs: With f < fs, negative reactance of capacitor C exceeds the positive reactance of inductor L. Hence the overall reactance of the circuit is capacitive. Current I leads the applied voltage V. Voltage VL leads the current by 90° The phasor diagram is shown in fig. 7.2b Case 2. f > fs: f> fs, the reactance of inductor L exceeds the reactance of With capacitor. The overall reactance is positive. Current lags the applied voltage V.The phasor diagram is shown in fig. 7.2c Reactance & Impedance curve of a series RLC circuit: the reactance and impedance of a series RLC circuit is shown in fig 7.3The reactance of inductor is: XL=ωL And its impedance ZL=jXL Thus the impedance of an inductor is always imaginary leading the resistor R by 90°.Curve(a) in fig. 5.3 shows the variation of XL with frequency. This is the straight line. The reactance of a capacitor is: XC=1/(wC) And its impedance: ZC=1/(j wC)=-j/( wC) Thus the impedance of a capacitor is always imaginary and lags behind the resistor by 90°. Curve(b) in fig. 7.3 shows the variation of Xc with frequency This is a hyperbolic curve. The impedance of L and C in series is: ZLC=j(XL-XC) This variation is illustrated by curve(c) in fig. 7.3 It has both positive and negative values depending upon whether AL is greater than or less than Xc. also this curve causes the frequency axis at ws which is the frequency of Series resonance. the impedance of the entire RL C circuit is: Z=R-j(XL-XC) Current I=V/Z=V/(R-j(wL − 1/ wC)) At resonance. The impedance Z becomes purely resistive. Thus wsL = 1/( wsC) At resonance using equation, the current is given by: I= V/R This condition is called series resonance. Series resonance at any desired frequency fs may be obtained by varying L or C or both. For fixed values of L and C, series resonance may be obtained by varying the frequency of applied signal. Phasor diagram of RLC circuit At f = fs, the reactance of inductor equals the reactance of capacitor, i. e. VL& VC cancel each other. The circuit is then purely resistive and the voltage V across the circuit is in phase with the current l (see fig. 7.2a) A B C Fig 7.2 phasor diagram of series RLC circuit Curve(d) in fig. 7.3 shows the nature of variation of Z with frequency At 𝜔 = 𝜔s Z= R. this is the minimum value of impedance. Fig.7.3 reactance and impedance plots of series RLC circuit Procedures: 1- connect the circuit shown in fig 7.1 2- set the output of function generator at 8 Vp.p, 200Hz (sine wave). 3- Vary the frequency of the function generator from 200 Hz – 600Hz in step of 50 Hz. Keep the output voltage constant 4- Record the reading of each measuring instruments shown in fig. 7.5 at each step. Note: Tabulate your results as shown in table 7.1 Calculation and graphs: 1- Evaluate the impedance of the circuit for each frequency. 2- Plot a graph of impedance and current against frequency. 3- Plot a graph of XL & XC against frequency on the same graph. 4- Plot a graph of phase shift angle against frequency. 5- Determine the value of resonance frequency from the graph obtained from step (2) and (3). 6- Determine the bandwidth of the circuit Discussion: 1- Why the series resonance is usually avoided in the circuit application. 2- Explain the effect of the value of R on the selectivity and bandwidth of the circuit. TABLE 7.1 measure values of I, VR, VL & Vc for each value of input waveform frequency.