# Homework #6 203-1-1721 ... Part A ```Homework #6
203-1-1721
Physics 2 for Students of Mechanical Engineering
Part A
20. What must be the diameter of an iron wire if it is to have the same resistance as a copper wire 1.19
mm in diameter, both wires being the same length? Use the table presented in lecture.
23. When a potential difference of 115 V is applied between the ends of a 9.66-m-long wire, the
current density is J = 1.42 A/cm2. Calculate the conductivity of the wire material.
27. For a hypothetical electronic device, the potential difference V, measured across the device, is
related to the current i by V = (3.55 x 106 V/A2)i2. (a) Find the resistance when the current is 2.40
mA. (b) At what value of the current is the resistance equal to 16.0 ?
28. Calculate the mean free time  between collisions for conduction electrons in aluminum at 20 C
using tables from the lecture. Each atom of aluminum contributes three conduction electrons. The
density of aluminum is 2.7 g/cm3 and it has a molar mass of 27 g/mol.
Part B
6. (a) The current density across a cylindrical conductor of radius R varies according to the equation j
= jo(1 - r/R) where r is the distance from the axis. Thus the current density is a maximum jo at the
axis r = 0 and decreases linearly to zero at the surface r = R. Calculate the current in terms of jo and
the conductor's cross-sectional area A = R2. (b) Suppose that instead the current density is a
maximum jo at the surface and decreases linearly to zero at the axis (center) so that j = jo r/R.
Calculate the current again. Why is this result different from that in (a)?
8. A common flashlight bulb is rated at 310 mA and 2.90 V, the respective values of the current and
voltage under operating conditions. If the resistance of the bulb filament when cold (To = 20C) is
1.12 , calculate the temperature of the filament when the bulb is on. The filament is made of
tungsten. Use the equations and tables presented in lecture.
10. A block in the shape of a rectangular solid has a cross-sectional area of 3.50 cm2, a length of 15.8
cm, and a resistance of 935 . The material of the block has 5.33 x 1022 conduction electrons per
m3. A potential difference of 35.8 V is maintained between its ends. (a) Find the current in the
block. (b) Assuming that the current density is uniform, what is its value? Calculate (c) the drift
velocity of the conduction electrons and (d) the electric field in the block.
14. A resistor is in the shape of a truncated right circular cone, as shown in Fig. 29-22 below. The end
radii are a and b, and the length is L. If the taper (slope) is small, we may assume that the current
density is uniform across any cross-section. (a) Calculate the resistance of this object. (b) Show that
your answer reduces to L/A for the special case of zero taper (a = b).
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