Physics 21
Fall, 2011
Solution to Hour Exam #1
The graders for the problems were:
1 Tupa, 2 Faust, 3 Beels, 4 Malenda, 5 Glueckstein
For questions about the grading, see the grader by Oct. 26.
Problem 1.
Consider the following circuit:
2
Ω
I
1
8V
12 V
6
Ω
7
Ω
I
2
I
3
ab
cd
loop 1
loop 2
(a) (13 pts.) Write Kirchho±’s loop and junction (or
node) equations needed to determine the currents
I
1
,
I
2
,and
I
3
.
Use the currents and their di
rections speci²ed by the arrows in the diagram.
You must write these equations as defned
in Physics 21.
You should have three equations
for three unknowns.
Draw clearly and label
on the diagram the loop used to determine
each loop equation.
(b) (3 pts.) Determine the currents
I
1
,
I
2
I
3
(in
cluding the correct sign) by explicit solution, by
hand, of the equations you determined in part (a).
You must show your work.
(c) (2 pts.) Use the currents you calculated in part
(b) to ²nd the potential di±erence
V
c

V
b
between
the corner points labelled
c
and
b
on the diagram,
using the path through corner point
a
. Show your
work, including the potential change across any
circuit elements on this path.
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 Spring '08
 Hickman
 Current, pts, Electric charge, Fundamental physics concepts, Gauss’ Law

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