A car owner forgets to turn off the headlights of his car while it is parked in his garage. If the 12.0-V battery in his car is rated at 150.0 A · h and each headlight requires 41.4 W of power, how long will it take the battery to completely discharge?
Calculate the amperage of the lights:
watts/volts= Amps.
Then divide the battery's capacity by the answer.
43.47
To find out how long it will take for the car battery to completely discharge, we need to calculate the total energy consumed by the headlights and divide it by the power capacity of the battery.
First, we need to convert the power requirement of each headlight from watts to amp-hours since the battery capacity is given in amp-hours.
Given:
Battery voltage (V) = 12.0 V
Battery capacity (C) = 150.0 A · h
Power per headlight (P) = 41.4 W
To convert watts to amp-hours, we can use the formula:
Energy (E) = Power (P) × Time (T)
Rearranging the formula, we can solve for Time (T):
Time (T) = Energy (E) / Power (P)
To calculate Energy (E), we need to convert Power (P) to Energy (E) and then sum it up for both headlights.
Energy (E) = Power (P) × Time (T)
Energy (E) = 41.4 W × T (in hours)
Now let's calculate the energy consumed by each headlight:
Energy per headlight = 41.4 W × T (in hours)
Since we have two headlights, the total energy consumed by both headlights is:
Total energy = 2 × (41.4 W × T (in hours))
Next, let's calculate the time it takes for the battery to completely discharge:
T = Total energy / Battery capacity
T = [2 × (41.4 W × T (in hours))] / 150.0 A · h
To solve this equation, we need to isolate the variable T:
Simplifying the equation, we get:
T = [2 × (41.4 W × T)] / 150.0 A · h
Now, we can solve for T. However, this equation is a little complicated to solve analytically due to the presence of T on both sides of the equation. To get an estimate of T, we can use numerical methods or approximation techniques.
Let's assume a value of T, say T = 1 hour.
Now we can substitute this assumed value of T in the equation to calculate T:
T = [2 × (41.4 W × 1 hour)] / 150.0 A · h
Calculating this, we get:
T = [82.8 W · h] / 150.0 A · h
T ≈ 0.552 hour
Therefore, it will take approximately 0.552 hours (or about 33.12 minutes) for the battery to completely discharge with the headlights left on.