The 30m extension cord is made of copper wire with a diameter of 1.3mm. What is the resistance

The 30m extension cord is made of copper wire with a diameter of 1.3mm. What is the resistance of the extension cord? What is the voltage drop across it if a current of 10A flows through it?

Data: l – length of the considered extension (l = 30 m); d is the diameter of the wire spent (d = 1.3 mm); I is the current in the extension cord (I = 10 A).

Const: ρm – beats. electrical resistance of copper (approx. ρm = 0.018 Ohm * mm2 / m).

1) Find the cross-section of the spent copper wire: S = 0.25 * Π * d ^ 2 = 0.25 * 3.14 * 1.32 ≈ 1.33 mm2.

2) Let’s calculate the resistance of each core: R = ρm * l / S = 0.018 * 30 / 1.33 ≈ 0.41 Ohm.

3) Find the resistance of the extension cord in question:

a) two current-carrying conductors: R2 = 2 * R = 2 * 0.41 = 0.82 Ohm;
b) three current-carrying conductors: R3 = 3 * R = 3 * 0.41 = 1.23 Ohm.

4) Determine the voltage drop:

a) U2 = R2 * I = 0.82 * 10 = 8.2 V;

b) U3 = R3 * I = 1.23 * 10 = 12.3 V.

Answer: The resistance of the extension cord in question is 0.82 ohms (1.23 ohms); voltage drop – 8.2 V (12.3 V).