Question

Define Kilowatt hour. How many Joules are equal to 1 kilowatt-hour? An electric kettle rated 220 volts, 2.2 kilowatts works for 3 hours. Calculate energy consumed and the current.

Hint:

To calculate energy consumed, use the formula \( E = P \times t \). For power in watts and time in hours, the energy in kWh can be converted to Joules by multiplying by \( 3,600,000 \).

Answer 1

Step 1: Definition of Kilowatt-hour.
A
kilowatt-hour (kWh) is the amount of energy consumed by a device with a power rating of 1 kilowatt operating for 1 hour. It is a unit of energy commonly used by electric utilities to measure electrical energy consumption. \[ 1 \, \text{kWh} = 1 \, \text{kilowatt} \times 1 \, \text{hour} \]
Step 2: Conversion of Kilowatt-hour to Joules. We know that: \[ 1 \, \text{kilowatt} = 1000 \, \text{watts} \quad \text{and} \quad 1 \, \text{hour} = 3600 \, \text{seconds} \] Thus, the energy in Joules for 1 kWh is: \[ 1 \, \text{kWh} = 1000 \, \text{watts} \times 3600 \, \text{seconds} = 3,600,000 \, \text{Joules} \] So, \( 1 \, \text{kWh} = 3,600,000 \, \text{Joules} \).
Step 3: Calculation of energy consumed by the electric kettle.
The power rating of the electric kettle is 2.2 kilowatts (kW), and it works for 3 hours.
Energy consumed \( E \) is given by the formula: \[ E = P \times t \]
where:
- \( P = 2.2 \, \text{kW} \) (power of the kettle),
- \( t = 3 \, \text{hours} \).
Thus: \[ E = 2.2 \, \text{kW} \times 3 \, \text{hours} = 6.6 \, \text{kWh} \] Now, convert energy to Joules: \[ E = 6.6 \, \text{kWh} \times 3,600,000 \, \text{Joules} = 23,760,000 \, \text{Joules} \]
Step 4: Calculation of the current.
The electric kettle operates at a voltage of 220 volts, and its power is 2.2 kW.
We can use the formula for electrical power: \[ P = V \times I \]
where:
- \( P = 2.2 \, \text{kW} = 2200 \, \text{W} \) (convert to watts),
- \( V = 220 \, \text{V} \) (voltage),
- \( I \) is the current.
Rearranging the formula to solve for current: \[ I = \frac{P}{V} = \frac{2200}{220} = 10 \, \text{A} \]
Step 5: Conclusion.
- The energy consumed by the electric kettle in 3 hours is
23,760,000 Joules.
- The current drawn by the electric kettle is
10 amperes.