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

Step-by-step 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 [ (1+cos2\omega t)/(2) \right ]`

`p\left ( t\right )=( V_mI_m)/(2)\left ( 1+cos2\omega t\right )`

`P_(avg)=( V_mI_m)/(2)`

`P_(avg)=(V_m^2)/(2r)`

`P_(avg)=(170^2)/(5.3* 2)=2726.41W`