Can You Calculate How Long it Takes to Drain a Car Battery with Headlights On?

[FredericChopin]

Homework Statement

The headlights on a car operate typically at 60 W and the parking lights typically at 5 W. Assuming that there are two main headlights and four parking lights, what length of time will it take to discharge a 60 Ah battery, if the lights are left on?

Homework Equations

I = Q/t

V = W/Q

P = W/t

P = I²*R

P = V²/R

P = IV

The Attempt at a Solution

I have gotten no where with this question.

All that I could do was find that the total power consumed by the lights:

P_T = (2*10) + (4*5) = 140 W

, and the charge of the battery:

1 Ah = 3600 C
∴ 60 Ah = 216,000 C

, and that's it.

I have tried simultaneous equations by substitution and elimination but that doesn't work because all of the equations are derived from the base equations I = Q/t, V = W/Q and P = W/t, so I end up getting P = P all the time.

Hint's anybody?

Thank you.

 

[TSny]

Not sure, but maybe you are suppose to assume that the voltage of the battery is the typical voltage for a car battery.

 

[ehild]

You need the voltage of the car battery to find the current. Look at Automotive battery - Wikipedia, the free encyclopedia, or just see the battery in your car...

ehild

Homework Statement

The headlights on a car operate typically at 60 W and the parking lights typically at 5 W. Assuming that there are two main headlights and four parking lights, what length of time will it take to discharge a 60 Ah battery, if the lights are left on?

Homework Equations

I = Q/t

V = W/Q

P = W/t

P = I²*R

P = V²/R

P = IV

The Attempt at a Solution

I have gotten no where with this question.

All that I could do was find that the total power consumed by the lights:

P_T = (2*10) + (4*5) = 140 W

, and the charge of the battery:

1 Ah = 3600 C
∴ 60 Ah = 216,000 C

, and that's it.

I have tried simultaneous equations by substitution and elimination but that doesn't work because all of the equations are derived from the base equations I = Q/t, V = W/Q and P = W/t, so I end up getting P = P all the time.

Hint's anybody?

Thank you.

 

[FredericChopin]

Hmm... It seems like it... Based on this link, which is the worked solution to the question.

Thank you TSny and ehild.

So much for "complex, challenging and novel"...

 

[Nickie]

Hello,

Thank you for your question. The calculation of how long it takes to drain a car battery with headlights on can be done using the formula P = IV, where P is power, I is current, and V is voltage.

First, we need to calculate the total power consumption of the headlights and parking lights. As you have correctly calculated, the total power consumption is 140 W.

Next, we need to calculate the current (I) that is drawn from the battery. This can be done using the formula P = IV. Rearranging the formula, we get I = P/V. Plugging in the values, we get:

I = 140 W / 12 V = 11.67 A

Now, we can use the formula I = Q/t to calculate the time it takes to drain the battery. Rearranging the formula, we get t = Q/I. Plugging in the values, we get:

t = 216,000 C / 11.67 A = 18,519 seconds

This is equivalent to approximately 5.14 hours. Therefore, it would take about 5.14 hours for the battery to drain if the headlights and parking lights are left on.

I hope this helps. Let me know if you have any further questions.