7/27/16 Faraday’s Law and Inductors Equipment Needed Part I AC/DC Electronics Laboratory, Pasco EM-8656 Coil, Pasco (400) SF-8610 Galvanometer, Cenco (analog) Lead, Banana w/ clips Magnet, Cow Power Supply, Fisher-EMD S44175-1 Battery Eliminator Resistance Decade Box, TENMA 727270 String, Black Equipment Needed Part II AC/DC Electronics Laboratory, Pasco EM-8656 Cable, BNC Banana Cable, BNC/Alligator Function generator, 10Mhz BK Precision 4017A Inductor 1mH (½Ω) or Cable, Passive BNC/Probe (2) Oscilloscope, Tektronix TDS 1002B Capacitor, 10 F Resistor, 100Ω Capacitor, 0.1 F Introduction Inductors and capacitors are the primary “passive” energy storage devices in electronics. When inductors and capacitors are wired together a resonant circuit is formed that is very useful in tuning in signals in devices such as radio and TV receivers. A time-varying current passing through an inductor produces a backEMF across the coil that can be measured. As a preliminary step we will first examine the minus sign in Faraday’s law, also known as Lenz’s law, with the aid of a bar magnet and a galvanometer. Part I Procedure 1. Wire the battery eliminator through the Resistance Substitution Apparatus (RSA) and to the galvanometer as shown in Figure 1 (next page.) Set the RSA on 100k . Set the Battery Eliminator to 6vdc. Caution: Double check your settings to make sure you don’t blow out the galvanometer. Turn on the power supply and verify which terminal current must flow into for the NRG 2426 99030483 Page 1 of 7 7/27/16 galvanometer to display a needle deflection to the right. Many of the galvanometers have been labeled by hand showing which terminal is plus. However, the galvanometer may have been labeled incorrectly. Your job is to check this labeling. Figure 1 Schematic and Physical Layout of Circuit to determine galvanometer polarity DC Galvanometer Resistance Decade Box 2. Record which terminal (right or left) causes a rightward needle deflection. Figure 2 Cow Magnet Suspended 3. Suspend the cow magnet with the black string as shown in Figure 2 and determine which end of the magnet is the north pole and north seeking pole. 4. Connect the induction coil (400 turn) directly to the galvanometer such that if current is flowing clockwise in the coil a rightward needle deflection occurs. The arrow on the coil indicates the direction of the winding. 5. Push the north end of the cow magnet into the coil as shown in Figure 3 on the next page. When the magnitude of the flux is increasing which way does the needle deflect (right or left)? Which way was current induced in the winding NRG 2426 99030483 Page 2 of 7 7/27/16 (clockwise or counter clockwise)? Figure 3 When the magnitude of the flux is decreasing which way does the needle deflect? Which way was the current induced in the winding? 6. Push the south end of the cow magnet into the coil. When the magnitude of the flux is increasing which way does the needle deflect? Which way was current induced in the winding? When the magnitude of the flux is decreasing which way does the needle deflect? Which way was the current induced in the winding? Results Part 1 1. Are your results consistent with Faraday’s law? 2. Are they consistent with Faraday’s law for all four cases? a. Flux into the coil and increasing b. Flux into the coil and decreasing c. Flux out of the coil but increasing in magnitude d. Flux out of the coil but decreasing in magnitude NRG 2426 99030483 Page 3 of 7 7/27/16 Part II Procedure Part IIA 1. Build the circuit shown in Figure 4 with the Pasco electronics laboratory. Your goal is to view the voltage across the function generator on the oscilloscope’s channel 1 and the voltage across the resistor on the oscilloscope’s channel 2. The oscilloscope has a great many knobs and settings so please have your instructor check your oscilloscope settings for you. The channels should be DC coupled and the trigger should be set to automatic. The channels may be viewed simultaneously in either alternate or chop mode. Make sure the invert switch is off and the vertical sensitivity fine vernier and time sweep fine vernier are in the locked position. Figure 4: Circuit to measure AC steady state response of inductor and resistor in series. Pasco Laboratory 1 mH A B 100 Ω C Attach Channel 1 probe to A Attach Channel 2 probe to B Ground for generator and both Probes is C NRG 2426 99030483 Page 4 of 7 7/27/16 2. Set the function generator to 1kHz with a 1 volt peak output. Record the amplitude of the voltage across the resistor. Record the phase shift (if any) between the two oscilloscope channels. Write down which waveform “leads” and which waveform “lags.” The wave form with peak occurring at earlier time is said to lead. Note that the measured phase shift in radians can be found from Phaseshift d peaks d cycle 2 Equation 1 where d peaks number of divisions between peaks of the two signals d cycle number of divisions for one cycle 3. Repeat Step 2 for 5 kHz, 25 kHz, and 125 kHz. Calculations and Results for Part IIA For each frequency tested answer the following: 1. What is the value of the peak current flowing in the circuit? What is the value of the RMS current flowing in the circuit? 2. What is the value of the inductive reactance at this frequency? What peak voltage ought to be across the inductor? What RMS voltage ought to be across the inductor? 3. Use the phasor diagram (Figure 5) below to derive the theoretical relationship between the voltage across the resistor and the voltage across the function generator. Note that in the diagram the voltage across the resistor and the current through the resistor are assumed proportional to cos t as discussed in class. Also find the theoretical relationship between the phase of the voltage across the resistor and the voltage across the function generator. NRG 2426 99030483 Page 5 of 7 7/27/16 Figure 5 Phasor diagram for LR circuit 4. Compare the theoretical and experimental values for the ratio of the peak voltage across the inductor to the peak voltage across the resistor. Compare the theoretical and experimental values for the phase shift between these two voltages. Which voltage leads? Procedure Part IIB 1. Modify the circuit on the Pasco Lab board to include a series capacitor as shown in Figure 6. Use the 0.01 F capacitor if it is available. Otherwise use a 10 F electrolytic capacitor. Figure 6 Circuit diagram for LCR circuit Pasco Laboratory 1 mH A C Attach Channel 1 probe to A Attach Channel 2 B probe to B 100 Ω Ground for generator and both Probes is C NRG 2426 99030483 Page 6 of 7 7/27/16 2. Compute the resonant frequency of the inductor and the capacitor from the formula: 1 LC res Equation 5 3. Compute the Q of the circuit from the formula: Q res L R Equation 6 4. Measure the ratio of the voltage across the resistor to the voltage across the function generator for several frequencies around resonance. Calculations and Results Part IIB Plot your results to Part IIB item 4 above. In particular plot the square of the voltage ratio vs. frequency. If the Q value is larger than 2 or 3 you should find Q res Equation 7 as discussed in your text. Does your plot indicate a Q value in agreement with the theoretical prediction? Conclusions Summarize your findings. Do the theoretical and experimental results agree? What percent error did you observe? Has the resistance of the coil had a big impact on the results? Why do you think this is the case? NRG 2426 99030483 Page 7 of 7