Download Recitation #10b Solution

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