# 1500w electric space heater problem

• tingling

## Homework Statement

*An electric resistance space heater rated at 1500W for a voltage source of v(t)=120√(2) sin(2pi60t)V has a thermostatically controlled switch. The
heater periodically switches on for 5 min and off for 7 min. Determine
(a) the maximum instantaneous power, (b) the average power over the
12-min cycle, and (c) the electric energy converted to heat in each 12-min
cycle.

none.

## The Attempt at a Solution

1. the maximum instantaneous power is twice of the rating right? 3000Watts?

2. and average power is the integral of instantaneous over time, divided by the time interval? but can't quite figure out what values to use.
3. for energy we use e=vit? am i supposed to multiply just the amplitudes of both voltage and current with time in seconds?

The power rating for an electrical appliance will be the RMS value so the peak input power (V2/R) will be twice as much.

For part 2) I would use the RMS value multiplied by the mark/space ratio eg

1500W * 5/12 = 635W

For part 3) you have a choice. You can either specify the number of Joules converted (remembering that a Watt is a Joule per second) or you can convert "635W for 12 min" to kWH. Both answer the question but I'd do both to be safe.

thanks cwatters.
much appreciated..