To estimate the electrical energy provided by the power company to an appliance, we need to follow a few key steps involving basic electrical formulas. Let's break it down step-by-step:
### Step 1: Calculate the Power in Watts
The power [tex]\(P\)[/tex] in an electrical circuit is given by the formula:
[tex]\[ P = V \times I \][/tex]
where [tex]\(V\)[/tex] is the voltage and [tex]\(I\)[/tex] is the current.
Given:
- Voltage [tex]\(V = 120\)[/tex] volts
- Current [tex]\(I = 2\)[/tex] amps
Substitute the values into the formula:
[tex]\[ P = 120 \, \text{V} \times 2 \, \text{A} \][/tex]
[tex]\[ P = 240 \, \text{W} \][/tex]
### Step 2: Convert Power to Kilowatts
Since 1 kilowatt (kW) is equal to 1000 watts (W), we need to convert the power from watts to kilowatts:
[tex]\[ P_{\text{kW}} = \frac{P_{\text{W}}}{1000} \][/tex]
[tex]\[ P_{\text{kW}} = \frac{240 \, \text{W}}{1000} \][/tex]
[tex]\[ P_{\text{kW}} = 0.24 \, \text{kW} \][/tex]
### Step 3: Calculate the Energy in Kilowatt-hours
Electrical energy [tex]\(E\)[/tex] can be calculated using the formula:
[tex]\[ E = P \times t \][/tex]
where [tex]\(P\)[/tex] is the power in kilowatts and [tex]\(t\)[/tex] is the time in hours.
Given:
- Power [tex]\(P = 0.24 \, \text{kW}\)[/tex]
- Time [tex]\(t = 4\)[/tex] hours
Substitute the values into the formula:
[tex]\[ E = 0.24 \, \text{kW} \times 4 \, \text{h} \][/tex]
[tex]\[ E = 0.96 \, \text{kWh} \][/tex]
### Conclusion
The electrical energy provided by the power company to the appliance in 4 hours is approximately:
[tex]\[ 0.96 \, \text{kWh} \][/tex]
