Question

An electric iron rated 1100 W, 220 V is operated for 5 hours.
Calculate:
(a) the minimum rating of the fuse required.
(b) the energy consumed in kWh.
(c) the cost of the energy consumed, if the rate is Rupees 10 per unit.

Hint:

To calculate electricity bills, always convert the power from Watts to Kilowatts (by dividing by 1000) before multiplying by the time in hours.

Answer 1

(a) Minimum rating of the fuse required:
Step 1: Formula to find the current. The current (\(I\)) drawn by the iron can be calculated from its power (\(P\)) and voltage (\(V\)) rating using the formula: \[ P = V \times I \] Step 2: Calculation. Given \(P = 1100\) W and \(V = 220\) V. \[ I = \frac{P}{V} = \frac{1100 \text{ W}}{220 \text{ V}} = 5 \text{ A} \] A fuse is a safety device with a rating slightly higher than the normal operating current of the appliance. Therefore, the minimum standard fuse rating required would be just above 5 A. However, the safe current limit for the appliance is 5 A.
(b) Energy consumed in kWh:
Step 1: Formula for energy consumption. The electrical energy (\(E\)) consumed is given by: \[ E = \text{Power} \times \text{Time} \] To get the energy in kWh (kilowatt-hours), the power must be in kilowatts (kW) and time in hours (h). Step 2: Unit conversion and calculation. - Power = 1100 W = \(\frac{1100}{1000}\) kW = 1.1 kW. - Time = 5 hours. \[ E = 1.1 \text{ kW} \times 5 \text{ h} = 5.5 \text{ kWh} \] (c) Cost of the energy consumed:
Step 1: Formula for cost. \[ \text{Cost} = \text{Energy Consumed (in units)} \times \text{Rate per unit} \] One unit of electrical energy is equal to 1 kWh. Step 2: Calculation. - Energy consumed = 5.5 units. - Rate = Rupees 10 per unit. \[ \text{Cost} = 5.5 \times 10 = \text{Rupees} \; 55 \]