Question

A particular wire has a resistivity of 2.7 x 10-82. m and a cross-sectional area of 4.3 x 10-6 m2. A length of this wire is to be used as a resistor that will develop 45 W of power when connected across a 20-V battery. What length of wire is required? km

Answer 1

We need to find the resistance of the wire.
The resistivity and resistance are related as
R = $\rho$ l / A
Where l is the length of the wire and A is that area of cross-section.
R = 2.7 x 10^-8 x l / 4.3 x 10^-6
R =  0.6279 x 10^-2 l
The power and the resistance are related as
P = V² / R
We need to find the length of the wire that would develop a power of 45 W when connected to a voltage of 20 V
45 = 20² / 0.6279 x 10^-2 l
l = 1415.64 m
l = 1.416 km