A portable electric heater uses 23.8 A of current. The manufacturer recommends that an extension cord attached to the heater receive no more than 2.60 W of power per meter of length. What is the smallest radius of copper (resistivity 1.72 x 10-8 Ω·m) wire that can be used in the extension cord? (Note: An extension cord contains two wires.)

P =I²R

R =ρL/A= ρL/πr²

P =I² ρL/πr²
r=sqrt(I² ρL/πP)=...

L=2 m, I=23.8 A, P=2.6 W,
ρ= 1.72 x 10 ⁻⁸ Ω

To determine the smallest radius of the copper wire that can be used in the extension cord, we need to calculate the resistance of the wire.

First, let's determine the power consumption of the heater in Watts (W). We know that power (P) is equal to current (I) multiplied by voltage (V): P = IV.

Since we are given the current (I) of 23.8 A, we need to find the voltage (V) supplied to the heater. Unfortunately, the voltage is not provided in the question. Without this information, we cannot calculate the power consumption of the heater accurately.

The information provided by the manufacturer about the recommended power per meter of length of the extension cord seems to be irrelevant to finding the radius of the wire. It is likely a distraction in this context.

Therefore, without the voltage information, we cannot calculate the power consumption, and consequently, we cannot determine the radius of the copper wire to be used in the extension cord.