A first year student is provided with a frequency generator, an inductor (L), a resistor (R),...

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A first year student is provided with a frequency generator, an inductor (L), a resistor (R), a capacitor, (C) and a power supply to investigate the resonance behaviour and the quality factor of a series RCL circuit. After connecting the circuit correctly and taking the potential difference across the resistor VR and the power supply, V as a function of the frequency f, using an oscilloscope (CRO), the following data was obtained. V (mV) VR (mV) Frequency (kHz) 50.2 571.4 2.954 3.206 72.0 547.6 132.4 428,6 3.524 103.2 500.0 3.390 150.4 365.1 3.598 175.4 162.1 253.6 3.745 321.2 3.865 123.2 452.1 4.045 515.2 96,03 4.210 79.19 539.5 4.352 39.68 579.4 5.130 23.00 587.1 6.138 15.08 589.0 8.225 41.27 579.2 2.785 587.3 16.66 1.790 15.4 587.5 1.340 1.000 12.3 591.0 For a resistor ofR-39.0 ± 0.5 2, inductor of L- 40.9 0.3 mH and capacitor of 45+ 0.4 nF (a) Sketch the RCL circuit for this experiment showing explicitly the electrical connections from the frequency generator and the CRO. [5 marks] Determine the resonance frequency of the LCR circuit using the graphical method, (b) [10 marks] Compare the experimental resonance frequency with the analytical value and (c) [4 marks] suggest the possible sources of error. (d) Determine the quality factor using the graphical analysis and discuss its variation [3 marks] from the analytical value. A first year student is provided with a frequency generator, an inductor (L), a resistor (R), a capacitor, (C) and a power supply to investigate the resonance behaviour and the quality factor of a series RCL circuit. After connecting the circuit correctly and taking the potential difference across the resistor VR and the power supply, V as a function of the frequency f, using an oscilloscope (CRO), the following data was obtained. V (mV) VR (mV) Frequency (kHz) 50.2 571.4 2.954 3.206 72.0 547.6 132.4 428,6 3.524 103.2 500.0 3.390 150.4 365.1 3.598 175.4 162.1 253.6 3.745 321.2 3.865 123.2 452.1 4.045 515.2 96,03 4.210 79.19 539.5 4.352 39.68 579.4 5.130 23.00 587.1 6.138 15.08 589.0 8.225 41.27 579.2 2.785 587.3 16.66 1.790 15.4 587.5 1.340 1.000 12.3 591.0 For a resistor ofR-39.0 ± 0.5 2, inductor of L- 40.9 0.3 mH and capacitor of 45+ 0.4 nF (a) Sketch the RCL circuit for this experiment showing explicitly the electrical connections from the frequency generator and the CRO. [5 marks] Determine the resonance frequency of the LCR circuit using the graphical method, (b) [10 marks] Compare the experimental resonance frequency with the analytical value and (c) [4 marks] suggest the possible sources of error. (d) Determine the quality factor using the graphical analysis and discuss its variation [3 marks] from the analytical value.