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Magazine Problem 23
A copper wire and an aluminum wire of the same length have the same
resistance. What is the ratio of the diameter of the copper wire to that of
the aluminum wire?
Problem 24
A bird sits on a high-voltage power line with its feet \(2.0 \mathrm{cm}\) apart. The wire is made from aluminum, is \(2.0 \mathrm{cm}\) in diameter, and carries a current of \(150 \mathrm{A}\). What is the potential difference between the bird's feet?
Problem 25
A person can be killed if a current as small as \(50 \mathrm{mA}\) passes near
the heart. An electrician is working on a humid day with hands damp from
perspiration. Suppose his resistance from one hand to the other is $1
\mathrm{k} \Omega$ and he is touching two wires, one with each hand. (a) What
potential difference between the two wires would cause a 50 -mA current from
one hand to the other? (b) An electrician working on a "live" circuit keeps
one hand behind his or her back. Why?
Problem 28
The resistance of a conductor is \(19.8 \Omega\) at \(15.0^{\circ} \mathrm{C}\)
and \(25.0 \Omega\) at \(85.0^{\circ} \mathrm{C} .\) What is the temperature
coefficient of resistance of the material?
Problem 29
A common flashlight bulb is rated at \(0.300 \mathrm{A}\) and \(2.90 \mathrm{V}\) (the values of current and voltage under operating conditions). If the resistance of the bulb's tungsten filament at room temperature \(\left(20.0^{\circ} \mathrm{C}\right)\) is \(1.10 \Omega,\) estimate the temperature of the tungsten filament when the bulb is turned on.
Problem 30
Find the maximum current that a fully charged D-cell can supply - if only
briefly-such that its terminal voltage is at least \(1.0 \mathrm{V}\). Assume an
emf of \(1.5 \mathrm{V}\) and an internal resistance of \(0.10 \Omega .\)
Problem 31
A battery has a terminal voltage of \(12.0 \mathrm{V}\) when no current flows.
Its internal resistance is \(2.0 \Omega .\) If a \(1.0-\Omega\) resistor is
connected across the battery terminals, what is the terminal voltage and what
is the current through the \(1.0-\Omega\) resistor?
Problem 32
(a) What are the ratios of the resistances of (a) silver and (b) aluminum wire
to the resistance of copper wire $\left(R_{\mathrm{Ag}} / R_{\mathrm{Cu}}
\text { and } R_{\mathrm{A}} / R_{\mathrm{Ca}}\right)$ for wires of the same
length and the same diameter? (c) Which material is the best conductor, for
wires of equal length and diameter?
Problem 33
A wire with cross-sectional area \(A\) carries a current \(I\) Show that the
electric field strength \(E\) in the wire is proportional to the current per
unit area \((I / A)\) and identify the constant of proportionality. [Hint:
Assume a length
\(L\) of wire. How is the potential difference across the wire related to the
electric field in the wire? (Which is uniform?) Use \(V=I R\) and the connection
between resistance and resistivity.]
Problem 35
Refer to Problem \(34 .\) With the copper wire connected to an ideal battery,
the current increases greatly when the wire is immersed in liquid nitrogen.
Ignoring changes in the wire's dimensions, state whether each of the following
quantities increases, decreases, or stays the same as the wire is cooled: the
electric field in the wire, the resistivity, and the drift speed. Explain your
answers.
