Inductors and L-R Circuits - Basic Physics Laboratory II | PHYS 2040, Lab Reports of Physics

Download Inductors and L-R Circuits - Basic Physics Laboratory II | PHYS 2040 and more Lab Reports Physics in PDF only on Docsity! 93 University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Name: _______________________ Date ____________ Partners ______________________________ Lab 6 – INDUCTORS AND L-R CIRCUITS The power which electricity of tension possesses of causing an opposite electrical state in its vicinity has been expressed by the general term Induction . . . Michael Faraday OBJECTIVES • To discover the effect of the interaction between a magnetic field and a coil of wire (an inductor). • To discover the effect of an inductor in a circuit with a resistor and voltage source when a constant (DC) signal is applied. • To discover the effect of an inductor in a circuit with a resistor and voltage source when a changing signal is applied. OVERVIEW You have seen that resistors interact with DC signals (currents or voltages) to produce voltages and currents which can be predicted using Ohm’s Law: RV IR= (1) You have also seen that the corresponding relationship for capacitors is /CV q C= (2) where q I t ∆= ∆ (3) 94 Lab 6 - Inductors and L-R Circuits University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Capacitors in RC circuits give predictable currents and voltages according to a different relationship. For the example of a discharging capacitor in an RC circuit, the voltage across the capacitor is given by 0 t RC CV V e −= . In this laboratory you will be introduced to yet another circuit element, the inductor (typically denoted by an L). An inductor is basically a coil of wire. A time varying magnetic flux ( )tΦ in such a coil induces a voltage across the coil according to N t ε ∆Φ= ∆ (4) where N is the number of turns in the coil, and ii B AΦ = ∆∑ (5) On the other hand, a current I flowing through a coil produces a magnetic flux proportional to I. So, a time varying current in a coil will generate a “back emf” I N N t I t ε ∆Φ ∆Φ ∆= = ∆ ∆ ∆ (6) We define the inductance L (more properly, the self inductance) as L N I ∆Φ≡ ∆ (7) Hence, the analog of Ohm’s Law for inductors is L I V L t ε ∆= = − ∆ (8) The negative sign represents the fact that the induced voltage will always be to avoid the changing magnetic flux. L is a constant whose value is a function of the geometry of the coil). Similarly, a second coil exposed to the field of the first will have a voltage 12 I V M t ∆= − ∆ (9) induced in it. M is called the mutual inductance and is a constant determined by the geometry of the two coils. Such coil pairs are called “transformers” and are often used to “step- up” or “step-down” voltages. Lab 6 -Inductors and L-R Circuits 97 University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 3. As illustrated above, hold the bar magnet outside the coil and begin graphing the voltage across the coil. Hold the magnet motionless outside the coil for a few seconds. Then move it fairly rapidly inside the coil. Hold the magnet motionless inside the coil for a few seconds. Finally, move it fairly rapidly outside the coil. Then stop graphing. 4. Flip the polarity of the magnet, i.e. turn the bar magnet around. Begin graphing and repeat the above sequence. Question 1-1: Summarize your observations. Describe the effects on the coil of wire when you have external magnetic fields that are a) steady (non-changing) and b) changing. Do your observations agree with your predictions? Prediction 1-2: Now consider the case where the bar magnet is held motionless but the coil is moved toward or away from the magnet. Predict what will be the reading by the voltage probe. Do this before coming to lab. Your TA will check early in the lab. 5. Choose one of the previous motions of the magnet (N or S pole pointing towards coil, and either moving magnet in or out.) Clear all data. Begin graphing the voltage across the coil. Repeat that motion of the magnet. Then, hold the magnet still and move the coil so that the relative motion between coil and magnet is the same. 98 Lab 6 - Inductors and L-R Circuits University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Question 1-2: Describe your observations. Is it the absolute motion of the magnet, or the relative motion between coil and magnet that matters? 6. Try to change the magnitude of the observed voltage by moving the magnet in and out faster and slower. Do it two or three times on the same display. 7. Print out the results. Question 1-3: What is the relationship you find between the magnitude of the voltage and the relative speed between the magnet and the coil? Explain. ACTIVITY 1-2: EXISTENCE OF A MAGNETIC FIELD INSIDE A CURRENT-CARRYING COIL. In the previous activity you used a permanent bar magnet as a source of magnetic field and investigated the interaction between the magnetic field and a coil of wire. In this activity you will discover another source of magnetic field--a current carrying coil of wire. Prediction 1-3: Consider the circuit in Figure 2 in which a coil (an inductor) is connected to a battery. Predict (and draw) the direction of the magnetic field at points A (along axis, outside of the coil), B (along the axis, inside the coil), and C (outside, along the side of the coil) after the switch is closed. [Hint: Consider the direction of the current flow.] Do this before coming to lab. Your TA will check. Lab 6 -Inductors and L-R Circuits 99 University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 switch V(battery) × • × × × × × × × × × × × × × × × × × × A B C × • • Figure 2 1. Connect the large coil, switch and 6-volt battery in the circuit shown in Figure 2. Place the coil on the table with its axis parallel to the table, i.e. on its side. 2. Close the switch. 3. Use the compass to map out the magnetic field and draw the field lines on the figure. Try enough locations to get a good idea of the field. 4. Open the switch. Do not touch metal when doing so or you may receive a small shock. Flip the polarity of the battery by changing the leads at the battery. Close the switch again and note the changes to the magnetic field. Just check a few positions. 5. Open the switch. Question 1-4: Clearly summarize the results. How do your observations compare to your observations of the magnetic field around the permanent magnet? What happened when you changed the battery polarity (direction of current)? Summary: In this activity you observed that a current-carrying coil produces a magnetic field. The magnitude of the magnetic field is largest in the center of the coil. Along the axis of the coil the direction of the magnetic field is aligned to the axis and points consistently in one direction. Outside the coil, the magnetic field is much weaker and points in a direction opposite to the magnetic field at the coil axis. 102 Lab 6 - Inductors and L-R Circuits University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Question 1-5: Make a general statement about the behavior of coils (inductors) based on your observations. Include in your statement the condition(s) under which a voltage is induced in a coil that is in the vicinity of another coil. We now want to see what will happen if we replace the battery and switch in Figure 4 with an AC voltage source. 4. Remove the battery and switch from the large coil, and instead connect the coil to the output of the PASCO interface (see Figure 5). A voltage probe (VPA) should still be connected to the small coil. 5. Open the experiment file L06.A1-2 Coil Voltage with AC. 6. With the small coil about a foot away, begin graphing and slowly move the small coil toward the large coil. When you're finished, leave the small coil approximately in the position of maximum signal, to be ready for the next activity. VPA PASCO Interface Output Figure 5 Lab 6 -Inductors and L-R Circuits 103 University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Question 1-6: Explain your observations. Comment on the phase relationship between the voltage driving the large coil, and the signal detected by the small coil. (Hint: When is the magnetic field of the large coil changing most rapidly?) Prediction 1-5: What do think will happen if we leave the coils motionless close together, and change the frequency of the AC voltage driving the large coil? [Assume that the frequencies are such that the amplitude of the current through the large coil remains constant.] Test your prediction. 7. Open the experiment file L06.A1-3 Coil Voltage vary Hz. (To avoid clutter, this will only graph the coil detector voltage and not the voltage driving the large coil.) 8. Set the frequency to 1 Hz and begin graphing. Repeat with a frequency of 2 Hz. The two sets of data will be on top of one another. Print one copy of your data for your group. Note: We use low frequencies so that the "self-inductance" of the large coil does not significantly impede the flow of current. 9. Move the detector coil away to prove that the signal is really from the large coil. 10. Try larger frequencies if you wish, but be aware that the amplitude of the current in the large coil will not be constant. 104 Lab 6 - Inductors and L-R Circuits University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Question 1-7: Describe your observations. Did the detected voltage change with driving frequency? How did its amplitude change? Explain why. Summary: In this investigation you have seen that a changing magnetic field inside a coil (inductor) results in an induced voltage across the terminals of the coil. You saw that such a changing magnetic field can be created in a number of ways: (1) by moving a magnet in and out of a stationary coil, (2) by moving a coil back and forth near a stationary magnet, and (3) by placing a second coil near the first and turning the current in the coil on and off, either with a battery and switch or with an AC voltage source. In the next investigation you will observe the “resistance” characteristics of an inductor in a circuit. INVESTIGATION 2: DC BEHAVIOR OF AN INDUCTOR Physically, an inductor is made from a long wire shaped in a tight coil of many loops. Conventionally, a symbol like is used to represent an inductor. In the simplest case we can model an inductor as a long wire. In previous investigations we approximated the resistance of short wires to be zero ohms. We could justify such an approximation because the resistance of short wires is very small (negligible) compared to that of other elements in the circuit, such as resistors. As you may know, the resistance of a conductor (such as a wire) increases with length. Thus for a very long wire, the resistance may not be negligible. All ‘real’ inductors have some resistance which is related to the length and type of wire used to wind the coil. Therefore, we model a real inductor as an ideal inductor (zero resistance) with inductance L in series with a resistor of resistance RL. A real inductor in a circuit then can be represented as shown in the diagram to the right, where the inductor, L, represents an ideal inductor. For simplicity, usually we let the symbol represent an ideal inductor while remembering that a real inductor will have some resistance associated with it. RL L Lab 6 -Inductors and L-R Circuits 107 University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 5. Measure the current and voltage as the switch is closed and opened, keeping it closed or opened for about a second each time. Question 2-1: Draw the current and voltage that you observe as you open and close the switch on the graph above. Explain how you agree or disagree with your predictions. 6. You should observe the current rising to its maximum value as follows: ( )max 1 tI I e τ−= − where the time constant L Rτ = is the time it takes the current to reach about 63% (actually 1 - 1/e) of its final value. Question 2-2: What value should you use for R? 7. Based on your redrawn circuit in step 2, calculate the expected time constant. L _____________ Rtotal _____________ Predicted time constant τpred: ____________ milliseconds Now use the Smart Tool to measure the maximum current on your graph, and the time it takes to reach 63% of that maximum. You will have to spread out the time scale. Measured time constant τexp: _____________milliseconds. 8. Replace the inductor by a resistor of (at least approximately) a value equal to the resistance of the inductor. Take data again, opening and closing the switch. 108 Lab 6 - Inductors and L-R Circuits University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 Question 2-3: What did you observe? Is there a fundamental difference between inductors and resistors? Explain. ACTIVITY 2-2: INDUCTORS IN SWITCHING CIRCUITS, MODIFIED ) You may have noticed in the previous circuit that, when the switch is opened the current decrease does not follow the normal L/R time constant. By opening the switch we are attempting to cut off the current instantaneously. This causes the magnetic field to rapidly collapse. Such a rapid change in the flux will induce a correspondingly large voltage. The voltage will increase until either the air breaks down (you can sometimes see or hear the tiny sparks) [or, if your tender fingers are a wee bit too close, you will make an odd yelping sound]. Figure 7. S1 is a push switch and S2 is a knife switch. To remedy this, we will modify the circuit ( Figure 7) so as to give the current somewhere to go. Note that the circuit is essentially the same as that for Activity 2-1, except that an extra wire and another switch (S2) have been added. We have also explicitly shown the battery's internal resistance, as we will need to consider its effects. We will now keep the push-type switch S1 closed during data taking. Its purpose will be to prevent the battery from running down when data are not being collected, so use the momentary contact switch here. It is switch S2 that we will be opening and closing during data taking. Set up the circuit in Figure 7. L + - V=6V S1 2 5 4 1 6 R CPB + - VPA + - S2 3 Rinternal Lab 6 -Inductors and L-R Circuits 109 University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 204, Spring 2008 Supported by National Science Foundation and the U.S. Dept. of Education (FIPSE), 1993-2000 For the following discussions we will assume switch S1 is always closed (connected) when taking data. However, switch S1 should be open (disconnected) when data are not being collected. Question 2-4: The figure on the left above shows the equivalent circuit configuration for Figure 7 when switch S2 is open (remember, switch S1 is closed). In this case we have assumed that Rinternal << R1 and so we can safely ignore it. In the space on the right above, draw the equivalent circuit configuration when switch S2 is closed (S1 is also closed). In this case, we cannot ignore Rinternal. In fact, this time we will assume that Rinternal is much larger than the resistance of the wires and the switches. Because the voltage induced across the inductor opposes an instantaneous change in current, the current flow through the inductor just after S2 is closed must be the same as the current flow through it just before S2 is closed. (If not, there would have been an instantaneous change in current, which cannot happen.) Prediction 2-2: Suppose that S2 has been open for a long time. In the first column of Table 2-1, predict the current in the circuit just before S2 is closed. Now predict in the second column of the table the current just after S2 is closed. Similarly, predict the current in the circuit just before S2 is opened (when S2 has been closed for a long time). Now predict in the fourth column the current just after S2 is opened. Do this before coming to lab. Discuss your reasoning with your tablemates in lab. L + - V 2 1 R1 CPB + - VPA + -