Stiebel Eltron
Please help me with this assessment ( Transformer )
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?
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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Luftwärmepumpe Stiebel Eltron Teil 1
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