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PHYS 212 – MT2
Summer 2012
Sample 2
Question 1
All resistors shown in the diagram are 30 . What is the resistance between points a and b?
A.
B.
C.
D.
E.
12 
15 
30 
25.7 
This combination cannot be reduced treating resistors in either series or parallel.
Question 2
A simple RC circuit consists of a battery (EMF ) a resistor (R) a capacitor (C) and a switch, all
in series. At time t = 0 the switch is closed. A long time after the switch is closed, the magnitude
of the current running through the resistor is:
A.
B.
C.
D.
E.

 R
2 R 
RC
None of the above
Page 1 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 3
A potential V(x,y,z) is plotted below. It does not depend on x or y.
What is the electric field E(x=-1 mm, y = 2mm, z = -5 mm)?
ˆi
2 NC ˆi
0
-2 NC ˆi
-5 N ˆi
A. 5
B.
C.
D.
N
C
E.
C
F. None of the above
Question 4
The electric field in some region of space points along the +x axis and decreases in magnitude as
x increases. The potential then:
A. is constant but non-zero on the x-axis.
B. decreases as x increases.
C. is zero everywhere on the x-axis.
D. increases as x increases.
E. none of the above.
Page 2 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 5
In the figure, starting at point a and proceeding counterclockwise, which loop equation is
correct?
A. 2V – i1 4 + 10V + i2 3 – i1 12= 0
B. –2V – i1 4 + 10V + i2 3 – i1 12 = 0
C. 2V – i1 4 – 10V + i2 3 – i1 12= 0
D. –2V – i1 4 + 10V – i2 3– i1 12= 0
E. 2V – i1 4 + 10V – i2 3 – i1 12= 0
Question 6
The graph in the figure shows the variation of the electric potential V (measured in volts) as a
function of the radial direction r (measured in meters). For which range or value of r is the
magnitude of the electric field the largest?
A) from r = 0 m to r = 3 m
B) from r = 3 m to r = 4 m
C) from r = 4 m to r = 6 m
D) at r = 3 m
E) at r = 4 m
Page 3 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 7
Suppose the current charging a capacitor is kept constant. Which graph below correctly gives the
potential difference V across the capacitor as a function of time?
A. I
B. II
C. III
D. IV
E. V
Question 8
In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (A,
B, C, D, E) will the bulbs be dimmest?
A.
B.
C.
D.
E.
F.
A
B
C
D
E
Two or more of these are tied
Page 4 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 9
Nine identical wires, each of diameter d and length L, are connected in parallel. The combination
has the same resistance as a single similar wire of length L but whose diameter is:
A. d/81
B. d/9
C. d/3
D. 3d
E. 9d
F. 81d
Question 10
Below is a graph of the x-component of the electric field along the x-axis. The potential is zero at
the origin. What is the potential at x  1m?
A.
B.
C.
D.
E.
F.
2000 V
1000 V
0V
-1000 V
-2000 V
None of the above
Page 5 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 11
All the capacitors in the figure have capacitance C = 1F, and the battery is a C (1.5 V) battery.
The capacitors are discharged initially, and then the switch is closed. How much total charge
does the battery deliver to the circuit after the switch is closed?
A.
B.
C.
D.
E.
F.
0.5 C
1.0 C
1.25 C
2.5 C
3.0 C
None of the above
Page 6 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Questions 12-13
The following 2 questions use the same set-up:
The below circuit is constructed with three identical resistors R, a capacitor C and a battery with
EMF . The switch is open for a long time.
Question 12
What is the current supplied by the battery just after the switch is closed?
A. 2
R

B.
R
2

C.
3R

D.
2R

E.
3R
F. 0
G. None of the above
Question 13
A long time after the switch has been closed, it is opened. What now is the current through the
capacitor?
A. 2
R
B. 
R
C. 2
3R
D. 
2R
E. 
3R
F. 0
G. None of the above
Page 7 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 14
For the circuit shown in the figure, I = 0.50 A and R = 12 Ω. What is the value of the emf ε?
A.
B.
C.
D.
E.
F.
6.0 V
12 V
18 V
24 V
48 V
None of the above
Question 15
Two uncharged conductors, A and B, are of different sizes. They are charged as follows:
1. A is charged from an electrostatic generator to charge q.
2. A is briefly touched to B.
3. Steps 1 and 2 are repeated until the charge on B reaches a maximum value.
If the final charge on B is 3q, what was the charge on A after the first time it touched B?
A.
B.
C.
D.
E.
F.
5q/6
2q/3
q/4
q/3
3q/4
None of the above
Question 16
Eight identical spherical raindrops are each at a potential V, where V=0 infinitely far away.
They coalesce to make one spherical raindrop whose potential is:
A. V/8
B. V/2
C. 2V
D. 4V
E. 8V
Page 8 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 17
The figure below shows equipotential lines in a potential landscape created by two large plates of
charge. A 5 mg, 10 mC point charge is moving vertically upward with a speed of 5 m/s at the
green dot (lower right of the picture). You guide it along the dark brown path by always pushing
perpendicular to its motion (doing no work!) until it reaches the red dot (upper left). How fast is
it going when it gets there?
A.
B.
C.
D.
E.
F.
0 m/s
1 m/s
5 m/s
7 m/s
It is impossible to tell given only the above information
None of the above
Question 18
An ideal parallel-plate capacitor consists of a set of two parallel plates separated by a very small
distance. The capacitor plates are charged to equal and opposite charges and are disconnected
from the battery used to charge them. In order to double the separation between the plates, you
do some work W (which could be positive or negative). How much energy was initially stored in
the capacitor?
A. -2W
B. -W
C. 0
D. W
E. 2W
F. None of the above
Page 9 of 10
PHYS 212 – MT2
Summer 2012
Sample 2
Question 19
A parallel plate capacitor with square plates (side length L) and plate separation d is initially
charged. We want to discharge it using a conductor of resistivity  shaped as a rectangular solid
that completely fills the region between the plates of the capacitor. What is the time constant 
that governs the discharge?
A.  
 0  L2
d2
0 d 2
B.  
L2
C.    0 
D.  
0

E. None of the above
Question 20
An ideal parallel-plate capacitor consists of a set of two parallel plates separated by a very small
distance. The capacitor plates are charged to equal and opposite charges ±q and are disconnected
from the battery used to charge them. At this point the capacitor is storing an unknown energy U.
A point charge of mass m and the same charge as the positive plate (q) is brought against the
center of the positively charged plate and released from rest. It accelerates towards the negative
plate, striking it with velocity v.
In terms of the given quantities (and fundamental constants) what was the energy U stored in the
capacitor?
2
A. U  14 mv
2
B. U  12 mv
2
C. U  mv
D. U  12 qv
E. U  qv
F. None of the above
Page 10 of 10