Please help me with this assessment ( Transformer )

Question

Please help me with this assessment

A STIEBEL ELTRON water heater model DHC4-3 is designed to operate at 277V AC to generate heat energy at a rate of 4.5kW. The main AC supply is sinusoidal with amplitude 312V at 50Hz.

(i) what is the turns ratio of the transformer required?

(ii) what is the resistance of the heater coil?

(iii) If the resistance of the heater coil increases by 1.08 times after 5 minutes of use due to the increase in temperature, what would be the rate of energy consumption (in kW) by the heater coil?

(iv) Assuming step-change in the resistance value and if the heater is operated for 8 minutes at a rate of cents 16.01 per 1kW-h, what will be the cost (in cents) incurred?

Answer 1

i) So you need a transformer to change 312 volts to 277 volts. This is a transformer with a turns ratio of 312 to 277

ii) P = E²/R

4500 = 277²/R

R = 17.05 ohms

iii) 17.05 x 1.08 = 18.41 ohms

P = E²/R = 277²/18.41 = 4167 watts

iv) Step change, so it operated 5 minutes at 4500 watts, which is

4500 W x 5 min x 1hr/60min = 375 W-hr or 0.375 kW-hr

(corrected error in line above)

The next 3 minutes, is is using 4167

4167 W x 3 min x 1hr/60min = 208 W-hr or 0.206 kW-hr

Adding the two, 0.583 kW-hr

multiplying by 16.01¢ = 9.3¢

edit: "retired", you could be right about the 312 volts, although it is usually listed as "312 volts peak". I always assume RMS unless stated otherwise. Found the arithmetic error, thanks.

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Answer 2

The above answer is good with clear explanation

Answer 3

"Sinusoidal with amplitude 312V" usually means the peak voltage is 312V. The RMS voltage would be 312/1.414 = 220.6, or 220V nominal supply voltage. "277V AC" usually means 277V RMS. You need a 220:277V transfromer or a 1:1.26 ratio.

It always pays to check the math. Everyone makes mistakes and the first answer that you received has at least one calculation error.