Download Physics 152 Test Review 3

Physics 251 Test Review 2
(12th edition)
Test 2 covers Chapters 23-30 of the text. There is a small amount of overlap with Test 1,
especially Chapter 22.
*
Capacitance calculations (Chapters 23, 24)
Step 1: calculate the electric field (E) from Gauss’ Law
Step 2: calculate the voltage difference between surfaces using
V = Edl
Step 3: find capacitance from C = Q/V
surface
text references/examples of steps 1,2,3:
Step 1
Step 2
infinite plane
cylinder
sphere
*
*
Ex. 22.8, p.765
Ex. 22.6, p.763
Ex. 22.5, p. 762
Ex. 23.9, p.796
Ex. 23.10, p. 797
Ex. 23-8 p795
Step 3
p.817
Ex. 24-4, p. 819
Ex. 24-3, p. 819
capacitor with dielectric constant, page 850ff
Resistivity of a rod (Ch. 25); see ,for example, Example 25-4, page 856
Direct Current circuits
- capacitors in series and parallel (compute charge, voltage, equivalent
capacitance)
- resistors in series and parallel (compute current, voltage, equivalent resistance)
- Kirkhoff’s Laws, junction and loop equations
*
magnetic field from a current density, Ampere’s Law (Section 28-7)
*
electromagnetic induction, slide wire
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LRC circuits (D.C. only)
*
charged particle motion; vector cross product (Section 27-4)
Copyright 2008, John R. Newport, Ph.D.
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Problem 1
Consider the circuit shown below. The Ri represent resistors. The gray highlighted letters
identify connection points. ε is an ideal voltage source.
E
A
^^^
R1
C
F
^^^
R2
^^^
R3
B
^^^
R4
^^^
R5
D
|
|ε|
|
a.)
Identify the number and location of each of the items below. Assume that the
resistances and source voltage are known.
Use the gray highlighted letters. Identify voltage drops across resistor Ri as Vi.
- How many nodes are there in this circuit? Where? ________________________
- How many loops possible? Where?
________________________
____________________________________________________________
- How many current variables are there?
________________________
- Is this system solvable? (i.e., can you solve
________________________
for all of the currents?) Why?
Copyright 2008, John R. Newport, Ph.D.
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b.)
Set up the loop and node equations using Kirkhoff’s Laws (but do not solve
them). Clearly identify the node or loop, including all directions, associated with each
equation.
DRAW EACH CURRENT ON THE DIAGRAM ABOVE, CLEARLY SHOWING ITS
DIRECTION!
Use the gray highlighted letters. Identify voltage drops across resistor Ri as Vi. (For
example, the voltage drop across R1 is V1.)
c.)
What is the algebraic method used for solving this system? (name?)
Copyright 2008, John R. Newport, Ph.D.
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Problem 2
A cylindrical conductor (radius R) has current flowing in the direction of its axis.
a.)
The current density is J(r) = Ae-(r/R). Find A in terms of the total current, I0. (Use
the definition of J.) Hint: xexdx = xex - ex
b.)
What is the magnetic field within the conductor, 0<r<R?
c.)
What is the magnetic field outside of the conductor, r>R?
d.)
What is the principle (law) used in these calculations?
Copyright 2008, John R. Newport, Ph.D.
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Problem 3
A slide wire (resistance R) travels without friction along the track shown below. It starts
from position x0 (non-zero) and velocity v0 , to the right as shown. Assume that the v
shaped rails meet at an angle of . Use the coordinate system shown.
The magnitude of the external magnetic field is constant. The direction of the external
magnetic field is also constant (into the page).
y
xxxxxxxxxxxx
xxxxxxxxxxxx
xxxxxxxxxxxx
x x x x x x x x x x x x
v0
x
a.)
State the principle that describes how to calculate the magnitude of the motional
electromotive force (this can be an equation).
b.)
State the principle that describes how to compute the direction of the current
associated with the electromotive force. (words)
c.)
Write the equation of the area enclosed in terms of x only. (Hint: What is the
equation of the slanted line? Write the slope in terms of .)
d.)
Find the induced electromotive force. This will be a function of both x(t) and v(t).
e.)
What is v(t)? (Algebraic equation for v(t).)
Copyright 2008, John R. Newport, Ph.D.
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