Watch out for units! Suppose a 19.1 V battery is connected to a long cylindrical

Question

Watch out for units!

Suppose a 19.1 V battery is connected to a long cylindrical wire, and a current of 1.93 A flows.

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

b) Find the total resistance of the wire.
RTOT = ____________

c) If the wire is 68.2 m long, and its diameter is 0.0542 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

Explanation / Answer

battery potential v=19.1 v

currrent in the wire i=1.93 A

a)

i=1.93 A

and

1A=1C/sec

1A=6.24*10^18 electorns/sec

no.of electrons for 1.93 A is,

n=1.93*6.24*10^18

n=1.2*10^19 electons/sec

b)

resistance R=V/i

=19.1/1.93

=9.89 ohms

c)

length of wire l=68.2 m

diameter d=0.0542 cm =5.42*10^-4 m

r=d/2 =2.71*10^-4 m

resistivity, rho =R*A/l

=R*pi*r^2/l

=9.89*(pi*2.71*10^-4)^2/(68.2)

=1.05*10^-7 ohm*m

d)

work done ,

w=q*V

=e*v

=1.6*19^-19*19.1

=1.54*10^-23 J

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