Question

An electric water heater has a rating of 1 kW, 230 V. The coil used as the heating element is 10m long and has a resistivity of 1.724 x 10^-6 ohm-cm. Determine the required diameter of the wire in mils?

Answer 1

$$Q=Pt=\frac{U^2}{R}t\\Q=mc_w(T'-T)+C(T'-T)\\=(C+c_wm)(T'-T)$$ $$\frac{U^2}{R}t=(C+c_wm)(T'-T)\\\frac{220^2}{20}120=(100+4200m)(100-40)$$ $$m=1.1\ kg$$