Page 294 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 24] ELECTRIC CURRENT 279

SOLVED PROBLEM 24.4
A 120-V toaster has a resistance of 12 . What must be the minimum rating of the fuse in the electric
circuit to which the toaster is connected?
The current in the toaster is
V 120 V
I = = = 10 A
R 12
so this must be the minimum rating of the fuse.

SOLVED PROBLEM 24.5
A 120-V electric heater draws a current of 25 A. What is its resistance?

V 120 V
R = = = 4.8
I 25 A
SOLVED PROBLEM 24.6

What potential difference must be applied across a 1200- resistor to produce a current of 0.05 A?

V = IR = (0.05 A)(1200 ) = 60 V

RESISTIVITY
The resistance of a conductor that obeys Ohm’s law is given by
L
R = ρ
A
where L is the length of the conductor, A is its cross-sectional area, and ρ (Greek letter rho), is the resistivity of
the material of the conductor. In SI, the unit of resistivity is the ohm-meter.
The resistivities of most materials vary with temperature. If R is the resistance of a conductor at a particular
temperature, then the change in its resistance R when the temperature changes by T is approximately
proportional to both R and T so that
R = αR T

The quantity α is the temperature coefficient of resistance of the material.

SOLVED PROBLEM 24.7

A 20-m length of a certain wire has a resistance of 15 . What length of this wire would have a resistance
of 8 ?

The resistance R of a wire is directly proportional to its length L. This means that the ratio between the
resistances R 1 and R 2 of two wires of the same kind and the same cross-sectional area equals the ratio between their
lengths L 1 and L 2 :

R 1 L 1
=
R 2 L 2
Here we solve this equation for L 2 and find that

R 2 8
L 2 = L 1 = (20 m) = 10.7m
R 1 15