On your first day at work as an electrical technician, you are asked to determin

Question

On your first day at work as an electrical technician, you are asked to determine the resistance per meter of a long piece of wire. The company you work for is poorly equipped. You find a battery, a voltmeter, and an ammeter, but no meter for directly measuring resistance (an ohmmeter). You put the leads from the voltmeter across the terminals of the battery, and the meter reads 12.4 V . You cut off a 20.0-m length of wire and connect it to the battery, with an ammeter in series with it to measure the current in the wire. The ammeter reads 7.10 A . You then cut off a 40.0-m length of wire and connect it to the battery, again with the ammeter in series to measure the current. The ammeter reads 4.20 A . Even though the equipment you have available to you is limited, your boss assures you of its high quality: The ammeter has very small resistance, and the voltmeter has very large resistance.

Part A What is the resistance of 1 meter of wire?

Will rate. Thank you!

Explanation / Answer

let internal resistance of battery be r

resistance of 20m wire = R (let)
now
R+r = voltage/current = 12.4 / 7.10 = 1.75

resistance of 40 m wire = 2R (as R is directly proportional to length)

now

2R+r = voltage/current = 12.4 / 4.20 = 2.95

so

R = (2R+r) - (R+r) = 1.206

R is for 20 m wire

for 1 m it is R/20 = 0.0603

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