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

Options

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

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Power of the Electric Kettle
The power \( P \) of the kettle can be calculated using the formula:
\[ P = V \times I \]
Where:
- \( V = 220 \, \text{V} \) (voltage)
- \( I = 4 \, \text{A} \) (current)

Substituting the values:
\[ P = 220 \, \text{V} \times 4 \, \text{A} = 880 \, \text{W} \]

### Step 2: Calculate the Heat Required to Boil Water
The heat \( Q \) required to raise the temperature of water can be calculated using the formula:
\[ Q = m \times C \times \Delta T \]
Where:
- \( m = 1 \, \text{kg} \) (mass of water)
- \( C = 4200 \, \text{J/kg°C} \) (specific heat capacity of water)
- \( \Delta T = T_{\text{final}} - T_{\text{initial}} = 100°C - 20°C = 80°C \)

Substituting the values:
\[ Q = 1 \, \text{kg} \times 4200 \, \text{J/kg°C} \times 80°C = 336000 \, \text{J} \]

### Step 3: Calculate the Time Required to Boil the Water
The time \( t \) required can be calculated using the formula:
\[ t = \frac{Q}{P} \]
Substituting the values:
\[ t = \frac{336000 \, \text{J}}{880 \, \text{W}} \approx 381.82 \, \text{s} \]

### Step 4: Convert Time from Seconds to Minutes
To convert seconds to minutes:
\[ t_{\text{minutes}} = \frac{t_{\text{seconds}}}{60} \]
Substituting the value:
\[ t_{\text{minutes}} = \frac{381.82 \, \text{s}}{60} \approx 6.36 \, \text{minutes} \]

### Final Answer
The time taken to boil 1 kg of water from 20°C to 100°C is approximately **6.36 minutes**.

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