Question

An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature $20^\circ C ?$ The temperature of boiling water is $100^\circ C $

• A. 12.6 min
• B. 4.2 min
• C. 6.3 min
• D. 8.4 min

Answer 1

The Correct Option is C

To solve this problem, we need to calculate how much time the electric kettle takes to boil 1 kg of water from 20°C to 100°C. Here's how to find the solution:

1. First, calculate the energy required to raise the temperature of 1 kg of water from 20°C to 100°C. This can be calculated using the formula for heat energy: Q = m \cdot c \cdot \Delta T, where:
   • m = 1 \, \text{kg} (mass of the water)
   • c = 4200 \, \text{J/kg}^\circ \text{C} (specific heat capacity of water)
   • \Delta T = 100^\circ C - 20^\circ C = 80^\circ C (temperature change)
   Plugging the values into the formula, we get: Q = 1\, \text{kg} \times 4200 \, \text{J/kg}^\circ \text{C} \times 80^\circ C = 336000 \, \text{J}
2. Next, calculate the power consumed by the electric kettle. Power is given by the formula: P = V \times I, where:
   • V = 220 \, \text{V} (voltage)
   • I = 4 \, \text{A} (current)
   Therefore, P = 220 \, \text{V} \times 4 \, \text{A} = 880 \, \text{W} (or 880 \, \text{J/s})
3. Finally, calculate the time required to boil the water using the formula: t = \frac{Q}{P}
   Substituting the values, we get:
   t = \frac{336000 \, \text{J}}{880 \, \text{J/s}} = 381.82 \, \text{s}
4. Convert the time from seconds to minutes: t = \frac{381.82}{60} = 6.36 \, \text{min}

Therefore, the time it takes for the electric kettle to boil 1 kg of water is approximately 6.3 minutes. Hence, the correct answer is 6.3 min.