Calculate the resistance of a piece of aluminum that is 20cm long and has
a cross-sectional area of 10-4m2. What is the resistance of a piece of glass
with the same dimensions? ρAl=2.82×10-8Ω.m, ρglass=1010Ω.m.
The resistance of aluminum
The resistance of glass
Notice that the resistance of aluminum is much smaller than glass.
A 0.90V potential difference is maintained across a 1.5m length of
tungsten wire that has a cross-sectional area of 0.60mm2. What is the
current in the wire?
From Ohm’s law
therefore,
(a) Calculate the resistance per unit length of a 22 nichrome wire of
radius 0.321mm. (b) If a potential difference of 10V is maintained cross
a1m length of nichrome wire, what is the current in the wire.
ρnichromes=1.5×10-6Ω.m.
(a) The cross sectional area of the wire is
The resistance per unit length is
(b) The current in the wire is
Nichrome wire is often used for heating elements in electric heater,
toaster and irons, since its resistance is 100 times higher than the copper
wire
A 2.4m length of wire that is 0.031cm2 in cross section has a measured
resistance of 0.24W. Calculate the conductivity of the material
Solution
A 0.9V potential difference is maintained across a 1.5m length of
tungsten wire that has cross-sectional area of 0.6mm2. What is the
current in the wire?
From Ohm's law,
A resistor is constructed by forming a material of resistivity ρ into the
shape of a hollow cylinder of length L and inner and outer radii ra and rb
respectively as shown in the figure. In use, a potential difference is
applied between the ends of the cylinder, producing a current parallel to
the axis. (a) Find a general expression for the resistance of such a device
in terms of L, ρ, ra, and rb. (b) Obtain a numerical value for R when
L=4cm, ra=0.5cm, rb=1.2cm, and ρ=3.5×105Ω.m.