PHY2049 Fall 2005
1
Prof. Andrew Rinzler
Prof. Paul Avery
Oct. 19, 2005
PHY2049, Fall 2005
Exam 2 Solutions
1. A wire made of a particular material has resistance
R
. Another wire made of the same material
that has 1/4 the length and 1/4 the diameter has resistance?
(1) 4
R
(2) 16
R
(3)
R
/ 2
(4)
R
/ 4
(5)
R
/ 16
Resistance is proportional to length and inversely proportional to crosssectional area. Since the
length is 1/4 of the old length and the area is 1/16 the old area, the new resistance is 4 times as
great or 4R.
2. A 2.00 kW heating element from a hair drier designed to operate at 120 V has a length of 80.0
cm. A 10.0 cm section of the element is removed. What power in watts is used by the now short
ened heating element at 120 V?
(1) 2290
(2) 1750
(3) 2250
(4) 1810
(5) need the resistivity
The new resistance R
new
is 7/8 the old resistance R. The total power, which is
2
new
/
V
R
, is thus
8/7 times the old power or 2290 W.
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2
3. For the circuit shown the resistors all have resistance
R
. The battery has internal resistance
r
.
What is the power dissipated by the battery?
(1)
()
2
2/
2
VR
r
+
(2)
2
4/
3
4
r
+
(3)
2
4
r
+
(4)
43 4
VR r
+
(5)
22
+
The total external resistance can be found from the rules of adding parallel and series resis
tances to be R / 2.
The total resistance is then r + R / 2.
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 Spring '08
 Avery
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