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A LED strip light uses about [tex]2.0 \, A[/tex] when operated on [tex]12.0 \, V[/tex]. At [tex]\$0.15[/tex] per [tex]kWh[/tex], what does it cost to run the light for 30 days?

Note: [tex]1 \, kWh = 3.6 \times 10^6 \, J[/tex]

A. \$8.64
B. \$1.86
C. \$6.46
D. \$0.86

Sagot :

GinnyAnswer
To determine the cost of running the LED strip light for 30 days, we should break down the problem step by step.

### Step 1: Calculate the power consumption
The power consumed by the LED strip light can be calculated using the formula:
[tex]\[ P = I \times V \][/tex]
where:
- \( I \) is the current in amperes (A),
- \( V \) is the voltage in volts (V).

Given:
- Current (\( I \)) = 2.0 A
- Voltage (\( V \)) = 12.0 V

Plugging in these values:
[tex]\[ P = 2.0 \, \text{A} \times 12.0 \, \text{V} = 24.0 \, \text{W} \][/tex]

### Step 2: Calculate the energy consumption over 30 days
To find out how much energy the LED strip consumes, we need to determine how many watt-hours (Wh) it uses. This can be done by multiplying the power by the total number of hours it runs.

Assuming the LED strip runs 24 hours a day for 30 days:
[tex]\[ \text{Energy} (\text{Wh}) = P \times \text{hours\_per\_day} \times \text{days} \][/tex]

Given:
- Power (\( P \)) = 24.0 W
- Number of hours per day = 24
- Number of days = 30

[tex]\[ \text{Energy} (\text{Wh}) = 24.0 \, \text{W} \times 24 \, \text{hours/day} \times 30 \, \text{days} \][/tex]
[tex]\[ \text{Energy} (\text{Wh}) = 24.0 \, \text{W} \times 720 \, \text{hours} \][/tex]
[tex]\[ \text{Energy} (\text{Wh}) = 17280.0 \, \text{Wh} \][/tex]

### Step 3: Convert energy consumption to kilowatt-hours (kWh)
Since electric energy is typically billed in kilowatt-hours (kWh), we convert watt-hours to kilowatt-hours:
[tex]\[ 1 \, \text{kWh} = 1000 \, \text{Wh} \][/tex]
[tex]\[ \text{Energy} (\text{kWh}) = \frac{17280.0 \, \text{Wh}}{1000} = 17.28 \, \text{kWh} \][/tex]

### Step 4: Calculate the running cost
Given that the cost of electricity is $0.15 per kWh, we can calculate the total cost of running the LED strip:
[tex]\[ \text{Cost} = \text{Energy} (\text{kWh}) \times \text{cost per kWh} \][/tex]

Given:
- Energy (\( \text{kWh} \)) = 17.28 kWh
- Cost per kWh = $0.15

[tex]\[ \text{Cost} = 17.28 \, \text{kWh} \times 0.15 \, \text{\[tex]$/kWh} = 2.592 \, \text{\$[/tex]} \][/tex]

Rounding this to two decimal places:
[tex]\[ \text{Cost} = \$2.59 \][/tex]

Therefore, the cost to run the LED strip light for 30 days is \$2.59.
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