The below is the problem statement


I have done as per my best knowledge and avoiding the mistakes, i got little confused in the end with the calculations for the complete cycle. Request to please review and any corrections.

Thank you in advance.

 

I think you over-complicated the duty cycle calculations. Integrating isn't wrong, but you already know the average power while the heater is on, the rated power. Now you have a duty cycle of 5 minutes on and 7 minutes off. The answer is simply 5/12 of what it would be if left on continuously.

Note that the answer you get is precise, for two reasons: 1) because you have an integral number of voltage cycles in both the on and off states. You get exactly 60 cycles per second and therefore an integral value (3,600) per minute and thus also per 5 or 7 minutes. 2) Even without #1, the size of any error due to a fractional part of the voyage wave would be tiny compared to the accumulated full waves, thousands of them, over 5 or 7 minutes.

 

Now you have a duty cycle of 5 minutes on and 7 minutes off. The answer is simply 5/12 of what it would be if left on continuously.

This will help to simplify my calculations in future problems.

Part C of the question how much electrical energy is converted to heat in each 12min cycle.
The answer is Energy = Avg Power (Watts) * Time (Hours) = 625 Watts * 12/60 Hours = 125 Watt Hour

I hope the above calculations are correct.

 

Part C of the question how much electrical energy is converted to heat in each 12min cycle.
The answer is Energy = Avg Power (Watts) * Time (Hours) = 625 Watts * 12/60 Hours = 125 Watt Hour

12 minutes is one fifth of an hour, so yes. Keeping track of units is a crucial. It's astounding how often you'll see watts and watt-hours confused.

 

It's astounding how often you'll see watts and watt-hours confused.

Along with Amps and Ampere-hours with a battery.