PHYS 222
Worksheet 10 – Current and
Resistivity
Leader: Alek Jerauld
Course: PHYS 222
Instructor: Dr. Paula Herrera-Siklódy
Supplemental Instruction
Iowa State University
Date: 2/7/12
Useful Equations
dQ
 n q vd A
dt
J  nqvd
E
J
I
R
L
A
General expression for current. Unit: Ampere [A]
Current density. Unit: [A/m2]
Resistivity does NOT depend on value of E field, it is a constant
Unit: [Ωm]
Geometric relationship between resistance and resistivity
Unit: Ohm [Ω]
V  IR
Ohm’s Law: Relationship among voltage, resistance and current.
Related Problems
1) A 5.50 A current runs through a 12-gauge copper wire (diameter 2.05 mm) and through
a light bulb. Copper has 8.5 x 1028 free electrons per cubic meter. (Book 25.3)
(a) How many electrons pass through the light bulb each second?
n  8.5(10)28 e  / m3
d 2
 33(107 ) m 2
4
I
vd 
 0.000123 m / s
nqA
A
 e 
19

 s   nvd A  3.4(10 ) e / s
 
(b) What is the current density in the wire?
I
J   1.67(106 ) A / m2
A
(c) At what speed does a typical electron pass by any given point in the wire?
I
vd 
 0.000123 m / s
nqA
2) The current is a wire varies with time according to the relationship: I = 55 A –(0.65 A/s2)t2
(a) How many coulombs of charge pass a cross section of the wire in the time interval
between t =0 and t = 8.1 s? (Book 25.7)
8.1
0.65 3
Q   Idt  55t 
t  330 C
3
0
(b) What constant current would transport the same charge in the same time interval?
Q
I ave  tot  41 A
ttot
3) What diameter must a copper wire have if its resistance is to be the same as that of an
equal length of aluminum wire with diameter 3.0 mm? (Book 25.18)
d 2
Ai  i , Lc  LA
4
i L
Ri 
, Rc  RA
Ai

c L
Ac

AL
AA
 dc  d A
c
 2.78 mm
A
4) In household wiring, copper wire 2.05 mm diameter is often used. Find the resistance of
a 24.0-m length of this wire. (Book 24.17)
L L
R
 2  0.125 
d
A

4
5) A rectangular solid of pure germanium measures 13 cm x 13 cm x 26 cm. Assume that
each of its faces is an equipotential surface. What is the resistance between opposite
faces? (Book 25.23)
 L 0.60(0.26)
Rlong 

 9.2 
A
(0.13) 2
 L 0.60(0.13)
Rshort 

 2.3 
A (0.13)(0.26)
6) A current-carrying gold wire has a diameter of 0.86 mm. The electric field in the wire is
0.51 V/m. (Book 25.25)
(a) What is the current carried by the wire?
I  kE d 2  12 A
(b) What is the potential difference between two points in a wire 6.6 m apart?
 L  gold L
R
 2
d 
A
4
V  IR  3.4V
(c) What is the resistance of a 6.6-m length of this wire?
 L  gold L
R
 2  0.28 
d 
A
4