Suppose a 98.1 V battery is connected to a long cylindrical wire, and a current

Question

Suppose a 98.1 V battery is connected to a long cylindrical wire, and a current of 2.19 A flows.

a) Find the number of electrons that pass any given point in the wire every second.

b) Find the total resistance of the wire.
RTOT = _____ ?

c) If the wire is 24.1 m long, and its diameter is 0.0167 cm, find the resistivity of the wire.
? = _____ ?-m

d) Find the work done by this battery to push one electron through the entire length of the wire.
W = _______ J

e) You will have three chances for this question.
A cylindrical wire of length L has resistance R = 527 ?. The wire is now passed through a die so it is drawn out to length 3.35L. What is the new resistance of the wire?
HINT: The length is not the only quantity that has changed!

Explanation / Answer

a)

Current I = q / t

q = I t = 2.19 C

Number of electrons N = q / e = 1.368*10^19 electrons

b)

Resistance

R = V / I = 98.1 V / 2.19 A = 44.79 ohm

c)

R = (resistivity ) L / A

resisitivity = R A / L

= (44.79 ohm ) pi (0.0167/2)^2 / ( 0.24 m )

=0.04810^-4 ohm-m

workdone W = q V = ( 1.6*10^-19 C ) ( 98.1 V) = 156.96 *10^-19 J

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