How to calculate "mean instant power"?

Question

I have an homework assignement that gives me an headache, I have a circuit with a 2000W heater with a all or nothing regulation using a thermostat

The heater is running 1/2 hour then stop for 1h from 6pm to 6am next day, so I calculated the duty cycle ratio (Time powered/(Time [s] powered + Time not powered) <=> (830)/((830)+(9*60)) which is 0.31.

I need to calculate the mean instant power of that circuit, I went to the conclusion that this value would be nominal power * duty cycle ratio but I'm not sure at all of that

Am I right with my calculation?

Answer 1

"Mean instant" is an oxymoron.

It is 2kW at the instant it is ON and 0 at the instant it is OFF.

But 0.5 h ON and 1 h OFF in a 1.5h cycle for any duration is 1/3 duty cycle so your mean power is 2/3 kW.

Answer 2

This isn't a complete answer because the question needs a bit of a clean-up.

The heater is running 1/2 hour then stop for 1h ...

That's a 1.5 hour duty-cycle

... for 6h straight (from 6pm to 6am next day)

6 p.m. to 6 a.m. is not 6 h. You need to fix that.

I need to calculate the mean instant power of that circuit,

Instant power is the power at any single time. This will be 2000 W or zero.

The mean power is the time averaged power.

I went to the conclusion that this value would be nominal power * duty cycle ratio but I'm not sure at all of that.

That's mean power, not "mean instant power".

Fix the 6 h straight bit and we'll try to answer.