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Transcript
Physics 212 Spring 2000 Recitation Activity #10: RC Circuits and B-fields NAME: Solution Instructor: Redwing DATE: March 9, 2000 This activity is based on the following concepts: RC circuits: when a capacitor is being charged or discharged, the charge on the capacitor, voltage across the capacitor and current in the circuit change exponentially with time; the change is characterized by a “time constant” = RC. a simple rule of thumb: when you make a change in an RC circuit (e. g. throw a switch), the voltage across a capacitor in the circuit CANNOT CHANGE ABRUPTLY! (Why not? Think about Q=CV, and I = dQ/dt = CdV/dt!). A magnetic field B is defined in terms of the FB acting on a test particle with charge q moving with velocity v: FB = qv x B In the circuit, switch S is initially open. Q1. Determine the value of the charge Q on the capacitor, the voltage V on the capacitor and the current I through the 20 resistor that is in parallel with the capacitor immediately after the switch is closed; Q=0 R1 = 20 100 F V=0 I=0A Q2. Determine the value of the charge Q on the capacitor, the voltage V on the capacitor and the current I through the 20 resistor that is in parallel with the capacitor a long time after the switch is closed. 120 V S R2 = 20 R3 = 20 Q = CV = (100 F)(40 V) = 4.0 mC V = 120 V/3 = 40 V I =120 V/ 60 = 2 A Q3. What is the time constant of the circuit, if R3 is removed from the circuit? = (20 100 F) = 4 msec Q4. Explain, without calculation, why the insertion of R3 would change the time constant of the circuit? Some of the current that would charge C without R3, flows through R3, but the dominant effect is the voltage. Initially, the current in the cap would be 120 V/40 . The final voltage across the cap is 40V, because of R3, instead of 120 V in the case without R3. So, although some of the current gets diverted through R3 to maintain an equal voltage drop in the parallel branch, the initial charging current is larger and the final charge is lower, i.e. more easily obtained. (NOTE TO GRADERS: Grade easy on this problem. Any attempt to explain should be counted correct. Q5. Particles 1, 2, and 3 follow the paths shown in the figure at right as they pass through the magnetic field there. What can one conclude about each particle? 1 +, 2 neutral, 3 - Q6. Of the three vectors in the formula F = qvxB, which pairs are always at right angles? Which may have any angle between them? F v, F B B, v can have any angle between them. Q7. Imagine that you are sitting in a room with your back to one wall and that an electron beam, traveling horizontally from the back wall toward the front wall, is deflected to your right. What is the direction of the magnetic field that exists in the room? down Q8. If an electron is not deflected in passing through a certain region of space, can we be sure that there is no magnetic field in that region? Why or why not? No, v can be parallel to B. Q9. If a moving electron is deflected sideways in passing through a certain region of space, can we be sure that a magnetic field exists in that region? Why or why not? No, might be an electric field. Scoring Guidelines: 100 90 75 60 40 0 All correct miss one some correct none to few correct, but shows effort Turned in paper, but no real effort No paper