Solution to Exam 2
Paul Avery, Art Hebard
PHY2049, Fall 2003
Oct. 20, 2003
1. Two 12 V batteries, A and B, are connected in series.
Battery A has an internal
resistance of 1
.
0Ω and battery B has an internal resistance of 0
.
5Ω.
What is the
effective voltage and internal resistance of the combination?
Solution:
When batteries are put in series, the equivalent EMF is the sum of the
voltages and the total resistance is the sum of the individual resistances.
Thus the
effective EMF is 24V and the internal resistance is 1.5Ω.
2. An infinitely long insulated wire carrying a current
I
is bent into the shape shown
(straight line plus circle of radius
R
with the currents in the direction shown). The
magnitude of the field
B
at the center of the circle is:
I
I
I
R
Solution:
The total field is the sum of the field from the infinite wire and the circle.
Taking into account the fact that the fields are in the same direction, we obtain
B
=
µ
0
I/
2
πR
+
µ
0
I/
2
R
=
µ
0
I
(
π
+ 1)
/
2
πR
.
3. Two currents, ﬂow at right angles as shown in the figure. What is the direction of the
force on wire segment B due to wire segment A?
A
B
1
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Solution:
Applying the right hand rule for the field from A, we see that it is going
into the page at location B. Using the force right hand rule for the current at B, this
gives a force acting in the upwards direction.
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 Spring '08
 Avery
 Physics, Resistance, Resistor, Electrical resistance, Series and parallel circuits, internal resistance

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