Question

The heating element in home electric furnace has a resistance of 5.3 ohms. It is connected to AC (alternate current) socket with maximal voltage 170 V. Find the average power consumed by the element.

Answer 1

Answer:2726.41 W

Explanation:

Consider the voltage and current in the form of

$v\left ( t\right )=V_mcos\omega t$

$i\left ( t\right )=I_mcos\omega t$

$p\left ( t\right )=\left ( V_mI_m\right )\left ( cos\omega t\right )^2$

$p\left ( t\right )=\left ( V_mI_m\right )\left [ \frac{1+cos2\omega t}{2} \right ]$

$p\left ( t\right )=\frac{ V_mI_m}{2}\left ( 1+cos2\omega t\right )$

$P_{avg}=\frac{ V_mI_m}{2}$

$P_{avg}=\frac{V_m^2}{2r}$

$P_{avg}=\frac{170^2}{5.3\times 2}=2726.41W$