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Chapter 10: Problem 3

A lead-acid automobile battery provides 12 V between its negative terminal and its positive terminal. It actually contains six individual batteries, connected in a chain. How much voltage does each individual battery provide?

Short Answer

Expert verified
Each individual battery provides 2 V.

Step by step solution

01

Understand the Total Voltage

The total voltage provided by the automobile battery is given as 12 V.
02

Identify the Number of Individual Batteries

The problem states that the battery contains six individual batteries connected in a chain.
03

Calculate the Voltage of Each Individual Battery

Since the total voltage is the sum of the voltages of the individual batteries, divide the total voltage by the number of individual batteries: \ \ \( V_{individual} = \frac{V_{total}}{6} = \frac{12\, V}{6} = 2\, V \)

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Key Concepts

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

Voltage Division
Voltage division is a principle used to understand how voltage is distributed across components in an electrical circuit, especially when they are connected in series.
In this exercise, the battery's total voltage of 12V is shared equally among the six individual batteries.
Each battery thus receives an equal fraction of the total voltage.
To find the voltage of each individual battery, we use the formula for voltage division, which is: \ \( V_{individual} = \frac{V_{total}}{n} \)
Here, \ V_{total} \ (12V) is divided by the number of individual batteries \ (n = 6) \.
This results in each battery providing 2V.
Series Connection
When components are connected in series, they are linked end-to-end in a single path for electric current to flow.
The same current flows through each component, but the total voltage is the sum of the voltages across each component.
In the case of our exercise, six individual batteries are connected in series to form a single 12V battery pack.
It's important to note that in a series connection:
  • Each component shares the same current flow.
  • The total voltage is the sum of voltages across all components.
  • If one component fails, the whole circuit is broken.

Through this connection, the individual batteries each provide 2V, adding up to a total of 12V.
Thus, the voltage of the entire battery pack is the sum of all individual voltages.
Electrical Circuit
An electrical circuit is a path through which electric current flows.
A circuit can be simple, like a single loop, or complex, with multiple loops and components.
In this exercise, the concept revolves around a simple series circuit created by six lead-acid cells.
Understanding electrical circuits involves knowing:
  • How components are connected (series or parallel).
  • How voltage and current behave within the circuit.
The lead-acid battery discussed here forms a series circuit where each cell contributes to the overall voltage.
Properly understanding the nature of electrical circuits helps in figuring out how multiple small voltage sources combine to form a larger total voltage.

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Most popular questions from this chapter

If you remove just one of the wires from an automobile’s battery, the vehicle will not start at all. Why doesn’t the other wire supply any energy?

Your skin has a much larger electrical resistance than your tissues. If you touch the two terminals of a battery with your fi ngers, where is the larger voltage drop—in your skin or in your tissues?

Your car has an electric defroster on its rear window. That defroster consists of 12 thin metal strips bonded to the inside surface of the glass. All the driver-side ends join together and all the passenger-side ends join together. When you switch on the defroster, current fl ows from the positive terminal of the battery to the driver-side end of the defroster and from the passenger- side end of the defroster to the negative terminal of the battery. Do the individual defroster strips form a series circuit or a parallel circuit?
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