What numbers and equations do I need to do this?

Question

A copper wire of length 20 cm and diameter 1.0 mm is heated at 20 degrees Celsius. The wire is hooked up to a 5.0 V potential difference. Determine (a) the resistance of the copper wire and (b) the current in the wire.

yeah, so where do i go with this?

Answer 1

the first answer leaves out one important factor and that is the temperature dependence of resistance

as the temperature of a wire increases, collisions inside the wire increase and cause an increase in resistance

you do want to calculate the current from Ohm's Law, i.e,



I=V/R

and you first need to calculate R.  But since they give you the temp, you also need to use the temp in calculating R.

The temperature dependence of resistance is given by:

R=R0[1+a(T-T0)]

where R is the resistance at some temp (here, 20 C)

R0 is the temp at a baseline temp (usually given as 0C)

a is the temperature coefficient of resistance (for copper, this is 3.9x10^(-3) / deg C)

and T-T0 is the temp difference between the current T and baseline T0 (probably 20 degrees)

so look up the resistance of copper and be sure you know what temp the value is relevant for, then use this equation to determine the temp at 20C...

so use the equation given in the first answer to find the resistance of this length and diameter wire (probably for 0 deg C), and then use this temp correction to get the resistance for 20C

hope this helps

Answer 2

Resistance =Resistivity x length/Area

current = voltage/ Resistance

look up the resitivity of copper and calculate the cross sectional area. then determine the resistance.

Then calculate the current flowing when hooked up to a 5.0 V potential difference.