Question

Problem 25.57

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 12.0 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 7.00 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 4.50 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.

What is the resistance of 1 meter of wire?in ohm

Answer 1

given

length of the wire 20 m

voltmeter reading 12.0 v, ammeter reading I1= 7.00 A, I2 = 4.5 A

resistance is proportional to length of the wire so resistnace of 1 m wire is  

                                R = V/20(1/ I2 - 1/ I1)

                                   = (12/20) ((1/ 4.5)- (1/ 7)

                                     = 0.047619 ohms

                                     = 4.7619 *10^-2 ohms