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BME 153 lab 4 capacitors inductors _Nigel

# BME 153 lab 4 capacitors inductors _Nigel - BME 153 Lab 4...

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BME 153 Lab 4 Lab 4 – Capacitors, Inductors and the Oscilloscope Nigel Chou Shijie Lab Partner: Tim Liu Section 1 October 10, 2007 I have adhered to the Duke Community Standard in completing this assignment. Objectives The objective of this lab is, firstly, to learn to use the oscilloscope and the function generator to find the amplitude and period of AC signals and the phase difference between two AC signals. Secondly, we learned to measure capacitance and inductance using a LCR meter. Thirdly, learned how to find the amplitude and phase difference of the voltage across resistors, capacitors and inductors with reference to the source voltage. Apparatus LCR Meter Fluke 45 Dual Display Digital Multimeter (DMM) BK Precision 1652 Triple Output Power supply Tektronic TDS 1012 Digital Storage Oscilloscope TGS 50 Signal generator Resistors, capacitor and inductor Procedure The procedure listed in the lab manual was followed with no deviation. Data and Calculations Resistor circuit with AC Source The voltages were calculated as follows: a R V V = 2 and b R V V = 4 . b a R V V V - = 3 a in R V V V - = 1 b in R V V V - = 5 The current was calculated by taking the voltage across each resistor and dividing by its resistance: R V I = The RMS voltage and current were obtained by taking the amplitudes and dividing by square root of 2: 2 of Amplitude V V RMS = and 2 of Amplitude I I RMS = The average power was obtained from the RMS values of Voltage and/or Current according to: R V P RMS 2 ) ( = or R I P RMS 2 ) ( = or ) )( ( RMS RMS I V P = All three methods give the same values. 1

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BME 153 Lab 4 Capacitors and inductors The % difference of the capacitance and inductance of circuit elements is calculated by: % 100 Value Nominal Value Nominal - value Measured diff % × = The phase shift of the voltages are calculated by: π 2 Period shift Time shift Phase × = The AC and DC currents are calculated from the voltage measured by the DMM by: R V I = Results Peak-to-Peak Voltage: 6.00 V Frequency: 1.002 kHz V in : 3.00 sin(2004πt) V a : 1.81 sin(2004πt) V b : 1.66 sin(2004πt) Table 1 : Current and Voltage across different resistors (R 1 to R 5 ) of Figure 1. Resistor Resistance ( ) Voltage (V) V rms (V) Current (mA) I rms (mA) Power dissipated (mW) R1 1000 1.19 sin(2004πt) 0.841 1.19 sin(2004πt) 0.841 0.708 R2 2000 1.81 sin(2004πt) 1.28 0.905 sin(2004πt) 0.640 0.819 R3 470 0.15 sin(2004πt) 0.106 0.319 sin(2004πt) 0.226 0.0239 R4 1500 1.66 sin(2004πt) 1.17 1.11 sin(2004πt) 0.782 0.919 R5 1800 1.34 sin(2004πt) 0.947 0.744 sin(2004πt) 0.526 0.499 Total: 2.968 Table 2 : Measured and nominal resistances of capacitor and inductor in circuits of Figure 2 and 3 Circuit Element Nominal Value Value measured with LCR Meter Percent Difference Capacitor (nF) 220 207.1 5.86% Inductor (mH) 4.7 4.493 4.40% Table 3 : Voltages and phase angles across the resistors in the circuit from Figure 2 and 3 Figure 2 (AC) Figure 3 (AC) V in (RMS) (V) 1.77 1.77 V a (RMS) (V) 0.636 1.15 V in - V a (V) 1.13 0.622
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