Question

The power rating of element used in electric geysers is between

• A. 10 to 100 W
• B. 100 to 500 W
• C. 500 to 1000 W
• D. 1000 to 3000 W

Hint:

A higher wattage rating means faster heating. Standard household electric geysers typically have heating elements rated at $2000\text{ W}$ ($2\text{ kW}$) or $3000\text{ W}$ ($3\text{ kW}$).

Answer 1

The Correct Option is D

Step 1: Thermodynamic Analysis of Water Heating:
Water has a remarkably high specific heat capacity ($c \approx 4184\text{ J/kg}^\circ\text{C}$). To raise the temperature of a standard volume of water (e.g., 10 to 25 liters) in a reasonable timeframe, a significant thermal energy input ($Q$) is required: $$Q = m c \Delta T$$ Where $m$ is the mass of water and $\Delta T$ is the change in temperature.

Step 2: Estimating Power Requirements:
The electrical power ($P$) must deliver this thermal energy over a time interval ($t$): $$P = \frac{Q}{\eta \cdot t}$$ Where $\eta$ represents the efficiency of the heating element. To heat household water efficiently, a domestic appliance must operate at high wattages.

Step 3: Evaluating Power Ratings of Appliances:

• $10\text{ to }100\text{ W}$: Appropriate for low-power electronics or incandescent light bulbs.
• $100\text{ to }500\text{ W}$: Appropriate for soldering irons or hand-mixers.
• $500\text{ to }1000\text{ W}$: Appropriate for dry electric irons or sandwich makers.
• $1000\text{ to }3000\text{ W}$ ($1\text{ to }3\text{ kW}$): Standard ratings for high-power thermal appliances like geysers, immersion rods, and electric kettles.

Therefore, option (D) is the correct choice.