Instructors house is maintained at a comfortable temperature

Instructor\'s house is maintained at a comfortable temperature by means of an electrical resistor heater during winter. The heater is operated at a constant current (I) under an applied voltage of 110 V. For simplicity, let us assume that the heater operates at a steady state, with 100% of conversion efficiency from the electrical energy to the internal energy of air in the house. Please find I if the instructor pays $11.80/day for heating, with electricity cost $0.11/kWh. Also, please calculate the heat produced by such a heater during a week.

Solution

In this problem, for heater bill is

a)

$ 11.80/day with electricity cost $0.11/kWh

cost for electricity per hour = 11.80/24 = $0.4916/hour

electricity spended = $0.4916/hour/$0.11/kWh = 4.4645 kW

now we know that

Power = VI

4.4645 * 1000 = 110*I

Therefore I = 4.0586 Amp

b)

Heat produced during a week =( heat produced/ second)*(week time)

= 4.464*7*24*3600 = 2699.827 kJ