Exercise EE1-04.05 – Conductor resistance and voltage drop of a cable reel

Prof. Dr. Thorsten Jungmann (last updated 2025-10-26)

Relates to EE1-04 Resistance

Task

From a large online department store, you order a $50\mathrm{m}$ cable reel of copper electric line with a cross-section of $1.5\mathrm{m}{\mathrm{m}}^2$ to operate the $2000\mathrm{W}$ electric heater in your garden shed. You notice that the heater in the garden shed does not heat as strongly as it does when you operate it at a socket-outlet in the house.

What technical cause could explain why the actual thermal power differs from the value stated on the packaging?

a) Sketch the electric circuit and locate the potential cause.

b) What is the conductor resistance of the cable reel at 20 °C?

c) Calculate the voltage drop across the electric line while the heater is operating. What voltage is actually applied to the heater?

d) What electric power does the heater draw, and how much does it emit as heat ($\eta =1$)?

e) Check your assumption from a).

f) Why should a cable reel always be fully unwound before operation?

Solution

$R_{\mathrm{line}}\approx 1.2\Omega$
$\Delta U_{\mathrm{line}}\approx 9.9\mathrm{V}$ → $U_{\mathrm{heater}}\approx 220.1\mathrm{V}$
$P_{\mathrm{heater}}\approx 1.83\mathrm{kW}$ (≈ 8.4 % below rated value)
$P_{\mathrm{line}}\approx 82\mathrm{W}$ (conductor loss)

▶️ Full worked solution