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Physics 213
HW #5 – Solutions
Spring 2009
26.23.
[Kirchoff’s Circuit Rules]
We have to use Kirchoff’s rules to find the unknown
currents, emfs, and resistances.
Apply the junction rule
at points
a, b, c
and
d
to calculate the unknown
currents. Then apply the loop rule to three loops to
calculate
12
,
and
.
R
The circuit is sketched to the right.
Apply the junction rule to point
a
:
3
3.00 A 5.00 A
0
I
3
8.00 A
I
Apply the junction rule to point
b
:
4
2.00 A
3.00 A
0
I
4
1.00 A
I
Apply the junction rule to point
c
:
3
4
5
0
I
I
I
5
3
4
8.00 A 1.00 A
7.00 A
I
I
I
As a check, apply the junction rule to point
d
:
5
2.00 A 5.00 A
0
I
5
7.00 A
I
(b)
Apply the loop rule to loop (1):
13
3.00 A 4.00
3.00
0
I
1
12.0 V
8.00 A 3.00
36.0 V
Apply the loop rule to loop (2):
23
5.00 A 6.00
3.00
0
I
2
30.0 V
8.00 A 3.00
54.0 V
(c)
Apply the loop rule to loop (3):
2.00 A
0
R
21
54.0 V 36.0 V
9.00
2.00 A
2.00 A
R
Finally, we can apply the loop rule to loop (4) as a check of our calculations:
2.00 A
3.00 A 4.00
5.00 A 6.00
0
R
2.00 A 9.00
12.0 V 30.0 V
0
18.0 V 18.0 V 0
26.50.
[Electric Dryer]
(a)
P
VI
I
2
R
,
so
I
P
V
4100 W
240 V
17.1 A. Recall from page 201 that 12gauge wire can carry up to 20A safely.
Thus, we can use 12gauge wire safely for this electric dryer.
(b)
2
V
P
VI
R
.
Solving for the resistance,
R
V
2
P
(240 V)
2
4100 W
14
.
(c)
At
11
c per kWH, for 1 hour the cost is
(11
c/kWh)(1 h)(4.1kW)
45
c .
(d)
It makes sense that the cost to operate the device is proportional to its power consumption.
The number also sounds
about right.
I am charged about one dollar to run a load of clothes through a dryer for an hour.
23.82.
[Alpha Particle Collision]
As the alpha particle moves from a to b, its total energy, kinetic plus potential, is conserved:
K
a
U
a
K
b
U
b
.
Assume the particles initially are far apart, so
U
a
0 , The alpha particle has zero speed at the distance of closest approach, so
K
b
0 .
Conservation of energy then gives
K
a
U
b
=11MeV.
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This note was uploaded on 04/14/2009 for the course PHYS 2213 taught by Professor Perelstein,m during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 PERELSTEIN,M
 Current, Magnetism, Resistance, Heat

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