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Chapter 23: Problem 46

The total charge that an automobile battery can supply without being recharged is given in terms of ampere-hours. A typical 12-V battery has a rating of 60 ampere-hours (60 A for 1 h, 30 A for 2 h, and so on). Suppose that you forget to turn the headlights off in your parked automobile. If each of the two headlights draws 3 A, how long will it be before your battery is 鈥渄ead鈥�?

Short Answer

Expert verified
The car battery will last for 10 hours before it is 'dead'.

Step by step solution

01

Understanding the Problem

We are given a 12-V battery with a total charge capacity of 60 ampere-hours. Two headlights are left on, each drawing 3 A. We need to know how long it will take for the battery to be completely discharged.
02

Calculate total current drawn by headlights

Since there are two headlights, and each draws 3 A, the total current drawn is calculated by adding the current of both headlights. The formula is: \( Total\text{ }Current = Current_{headlight1} + Current_{headlight2} \).
03

Determine the battery life

The battery life can be calculated by dividing the battery's total charge (in ampere-hours) by the total current drawn by the two headlights. The formula is: \( Battery\text{ }Life = \frac{Total\text{ }Charge}{Total\text{ }Current} \).
04

Perform the calculation

Using the formula from Step 3, we have \( Battery\text{ }Life = \frac{60\text{ }Ah}{6\text{ }A} \). Calculate the battery life to find out how long it will be before the battery is dead.
05

Conclusion

Solve the equation from Step 4 to determine the battery life in hours until the battery is considered 'dead'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Current
Electric current is the flow of electric charge, typically measured in amperes (A). In simpler terms, it's like the flow of water through a pipe; here, the 'water' is actually electrons moving through a conductor, like the wires that connect to the headlights of a car. The current tells us how substantial this flow is at any given moment.

Determining Current in Circuits

  • For a single device, the current is simply what the device draws.
  • In circuits with multiple devices, like our two headlights, we add the currents together if they're in parallel, as in this scenario.
In the given exercise, the current each headlight draws is 3 amperes. Therefore, for both headlights operating together, the total current drawn from the battery is 6 A.
Battery Capacity
Battery capacity is a measure of the charge a battery can hold, typically expressed in ampere-hours (Ah). It's similar to a fuel tank in a car: the capacity tells you how much 'fuel' you have to run electrical devices before needing a 'refill' 鈥� or, in this case, a recharge.

Understanding Ampere-Hours

  • A battery with a capacity of 60 Ah can supply 60 A for 1 hour, 30 A for 2 hours, and so on.
  • The capacity allows us to calculate how long a battery can keep running a certain load before depleting.
From the exercise, the battery has a capacity of 60 Ah. This is essential for figuring out how long the headlights can stay on before the battery runs 鈥榙ead鈥�.
Circuit Calculations
Circuit calculations involve using mathematical formulas to understand the behavior and requirements of electrical circuits. Key concepts are the voltage, current, resistance, and power relationships given by Ohm's Law and the power equations.

Finding Battery Life

  • The life of a battery under a given load is calculated by dividing the battery's total capacity by the total current.
  • This gives us the time the battery can sustain that load until it is completely discharged.
In reference to our exercise, after calculating the total current the headlights draw (6 A), we use the battery鈥檚 capacity (60 Ah) to determine the battery life, resulting in a straightforward division: 60 Ah 梅 6 A equals 10 hours of operation before the battery is exhausted.

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Most popular questions from this chapter

Why does a wire that carries electric current become hot?

The wattage marked on a lightbulb is not an inherent property of the bulb but depends on the voltage to which it is connected, usually 110 V or 120 V. How many amperes flow through a 60-W bulb connected in a 120-V circuit?

Calculate the power of a hair dryer that operates on 120 V and draws a current of 10 A.

Your friend says that a battery supplies the electrons in an electric circuit. Do you agree or disagree? Defend your answer.

In periods of peak demand, power companies lower their voltage. This saves them power (and saves you money!). To see the effect, consider a 1200-W coffeemaker that draws 10 A when connected to 120 V. Suppose the voltage is lowered by 10% to 108 V. By how much does the current decrease? By how much does the power decrease? (Caution: The 1200-W label is valid only when 120 V is applied. When the voltage is lowered, the current is lowered, so the power output of the toaster鈥檚 heating coils drops, which cools the coil and lowers its resistance. However, for this problem assume the change in resistance is slight.)
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