An electric heater of power 2500 W is connected to a voltage of 230 V.
i) Calculate the electric current going through the heater.
ii) What is the resistance of the heater?
iii) How much energy does it consume in a year, if it is switched on 15 min every day.
iv) How much it costs per year to use the heater when the price of electricity is 0,0479 €/kWh?
1. P = E*I= 2500.
230I = 2500, I = 10.9A.
2. R = E/I.
3. T = 365 * 15/60 = 91.25 h/yr.
4. Energy = kW * h = 2.5 * 91.25 = 228.125 kWh.
Cost = 0.0479/kW * 228.125kWh =
To answer these questions, we can use the formulas and relationships between power, voltage, current, resistance, energy, and cost.
i) Calculate the electric current going through the heater.
The formula to calculate the electric current is:
Current (I) = Power (P) / Voltage (V)
Plugging in the given values:
Current (I) = 2500 W / 230 V
Calculating the current:
Current (I) = 10.87 A (rounded to two decimal places)
Therefore, the electric current going through the heater is approximately 10.87 A.
ii) Calculate the resistance of the heater.
The formula to calculate resistance is:
Resistance (R) = Voltage (V) / Current (I)
Plugging in the given values:
Resistance (R) = 230 V / 10.87 A
Calculating the resistance:
Resistance (R) = 21.18 Ω (rounded to two decimal places)
Therefore, the resistance of the heater is approximately 21.18 Ω.
iii) Calculate the energy consumed in a year.
The formula to calculate energy consumed is:
Energy (E) = Power (P) * Time (t)
Given that the heater is switched on for 15 minutes every day:
Time (t) = 15 min/day
Converting time to hours:
Time (t) = 15 min/day * (1 hr / 60 min) = 0.25 hr/day
Assuming there are 365 days in a year:
Energy (E) = 2500 W * 0.25 hr/day * 365 days/year
Calculating the energy consumed:
Energy (E) = 228125 Wh (watt-hours) = 228.125 kWh (kilowatt-hours)
Therefore, the heater consumes approximately 228.125 kWh of energy in a year.
iv) Calculate the cost per year to use the heater.
The formula to calculate cost is:
Cost = Energy (E) * Price (P)
Given that the price of electricity is 0.0479 €/kWh:
Cost = 228.125 kWh * 0.0479 €/kWh
Calculating the cost:
Cost = 10.936875 € (rounded to two decimal places)
Therefore, it costs approximately 10.94 € per year to use the heater when the price of electricity is 0.0479 €/kWh.