Question

How much 1.0 mm diameter copper wire would it take to equal the resistance of one 100 Ω resistor? The resistivity of copper is 1.68*10-8 Ωm

b) What would be the current if this wire was connected to a 12.0 V battery?

c) How many electrons per second pass by a point on the wire?

d) If this wire was coiled up and submerged in 100 mL of water at 20oC, how long would it take for the water to boil? CH2O = 4186 J/kgC

Answer 1

The resistance of a wire having resistivity , length l and area of cross section A, is given by

.................... (1)

The given copper wire has a diameter of 1.0 mm. So, the area of cross section of the wire is

Putting all the given values in equation (1), we get

or,

or,

b.

​Using Ohm's law, the current in the wire is

c.

A current of 0.12 A is flowing through the wire, it means 0.12 C charge is flowing per second through a cross section of wire.

So, total number of electrons passing through the wire each second is

d.

Total heat required to change the temperature of 100 mL (0.1 kg) water from 20° to 100° C is

The heat released by a current conducting wire is given by

We can rewrite this equation as

Where all the symbols has their ususal meaning.

Therefore, for the given wire, the time required to generate a heat of 33488 J is