A 2.0-mm-diameter wire formed from a composite material has a resistivity that decreases with distance along the wire as ρ=ρ₀e^−αˣ, where ρ₀=4.0×10^−5 Ω m , x (in m) is measured from one end of the wire, and the constant α=4.0 m^−1. What is the resistance of a 50-cm-long length of this wire?

A resistor has a current through it of 5 A. If the EMF across the resistor is 10 V, what is the resistance of this resistor?

Two resistors are made of the same material, one twice as long as the other. If the current through the shorter resistor is 5 A, what is the current through the longer resistor if they both have the same potential difference and cross-sectional area?