1 Calculate the resistance per unit length of a thin 22gauge

1. Calculate the resistance per unit length of a thin 22-gauge Nichrome wire which has a radius of 0.375 mm. If a potential difference of 15V is maintained across a 1.0 m length of the Nichrome wire, what is the current of the wire?(Answers below)

cross-sectional area of the wire = 0.000000442 m^2

resistance per unit length = 3.39 ohm/m.

I=4.424

Using the same problem, calculate the electric field in the wire assuming that the wire carries a current of 7.9 A.

E= --------- N/C

(Hint: answer is not 15)

Solution

Resistivity of Nichrome = 110 * 10^-8 ohm.m

r = 0.375*10^-3 m

V = 15 V

L = 1.0 m

R = rho*L/A

I = V/R = V*A/rho*L = 15*3.14*0.375^2*10^-6/(110*10^-8*1) = 6.021 Amp.

B.

E = rho*J = rho*I/pi*r^2

E = 110*10^-8*7.9/(3.14*0.375^2*10^-6) = 19.68 N/C