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Wentworth Institute of Technology Department of Electronics and Mechanical ELEC 195 - Circuits Theory II Name: Date: Experiment 5 Using a Current Sensing Resistor to Find the Inductive and Capacitive Load Impedance Objective: 1. To learn how to calculate the resistance and reactance of elements using a currentsensing resistor. 2. To become familiar with the oscilloscope as a voltage-measuring instrument. Equipment Required: Resistor: Capacitor: Inductor: Leads: Jumpers A breadboard 100 1 F 10 mH 1 set of banana-to-clip leads and 2 sets of BNC-to-clip leads Resume of Theory: Impedance in the frequency domain is the quantity analogous to resistance, inductance and capacitance in time domain. The imaginary part of the impedance is called reactance. The reactance of an inductor or capacitor is a function of the applied frequency as defined by the followings 1 .c X L .L Xc where 2f rad/s , L =the inductance (H) and C = the capacitance (F) The inductor and capacitor impedances in rectangular forms are: Zc = - j X c ZL = j X L and in polar forms ZL = |XL|90o Zc = |Xc|-90o 1 Note: Ideally, internal resistance of an inductor is zero; however, a real life inductor has small resistance, and some cases the resistance is high enough that cannot be ignored. So, in this case, the impedance of an inductor is: ZL = RL + j XL Where RL is the internal resistance of the inductor and X L is the inductive resistance Procedure: PART I: a) Capacitive Load Construct the circuit shown below (Fig 4.1) Fig. 4.1 b) Measure the sensing resistor Rs = ______________ c) Set the voltage Vc to 4 Vpp and measure the RMS value of VRs VRs = ______________ d) Calculate VRS-pp VRS-pp = ____________ e) Calculate Ipp Ipp = _______________ 2 f) Xc Calculate the capacitive reactance Vcpp Ipp Xc (from measured values)= _________________ g) Measure the actual capacitance of the capacitor using the bridge. C = _____________ h) Using the capacitance value measured in part g, calculate the capacitive reactance of the circuit. Xc (calculated) = ___________ i) Compare the capacitive reactance in part f and h, and find the percentage of error between the two values. Comment on your results. j) Raise the source frequency to 400 Hz, and repeat part I. Compare the new capacitive reactance with the one found before. Comment on the results k) Draw the vector diagram and to find the impedance seen by the source for each frequency. PART II: Inductive Load a) Construct the circuit shown below (Fig. 4.2). b) Measure the sensing resistor Fig. 4.2 Rs = ______________ 3 c) Set the voltage VL to 1 Vpp and measure the RMS value of VRs VRs = ______________ d) Calculate VRS-pp VRS-pp = ____________ e) Calculate Ipp f) Calculate the inductive impedance | Z L | Ipp = _______________ VLpp Ipp |ZL| (from measured values)= _______________ g) Measure the actual inductance of the inductor using the bridge. L = _____________ h) Using the inductance value measured in part g, calculate the inductive reactance of the circuit. XL (calculated) =ω.L= ___________ Using the DMM measure the internal resistance of the inductor. RLint = ________________ Calculate the ZL |ZL|(calculated) = RLint + j XL = ( RLint X L = ____________ 2 2 i) Compare the inductive impedance (ZL) in part f and h, and find the percentage error between the two values. Comment on your results. j) Drop the source frequency to 1 KHz, and repeat part II. Compare the new inductive reactance with the one found before. Comment on the results k) Draw the vector diagram and to find the impedance seen by the source for each frequency. 4