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Chapter 4: Problem 7

Standard automobile batteries have six lead-acid cells in series, creating a total emf of \(12.0 \mathrm{~V}\). What is the emf of an individual lead-acid cell?

Short Answer

Expert verified
EMF of individual cell is 2.0 V.

Step by step solution

01

Identify the Total EMF and Cell Count

The total electromotive force (emf) of the automobile battery is given as \( 12.0 \text{ V} \). The battery consists of 6 cells connected in series.
02

Understand Series Connection of Cells

In a series connection, the total emf of the battery is the sum of the emfs of each individual cell. Hence, if we have \( n \) cells, each cell contributing an emf of \( E \), then: \( ext{Total emf} = n \times E \).
03

Calculate the EMF of One Cell

Given \( n = 6 \) (the number of cells in series) and \( ext{Total emf} = 12.0 \text{ V} \), use the formula \( 12.0 \text{ V} = 6 \times E \) to find \( E \). Thus, \( E = \frac{12.0 \text{ V}}{6} = 2.0 \text{ V} \).
04

Verify the Solution

Multiply the emf of the individual cell \( 2.0 \text{ V} \) by 6 to check the total emf: \( 6 \times 2.0 \text{ V} = 12.0 \text{ V} \), confirming that our calculation is correct.

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Key Concepts

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

Series Circuit
A series circuit is a configuration where components are connected end-to-end in a single path for the flow of current. In the context of batteries, the positive terminal of one cell is connected to the negative terminal of the next, creating a chain. This arrangement has key characteristics:
  • Single Path: There is only one path for the flow of electrons. A break at any point stops the entire circuit from carrying current.
  • Cumulative Voltage: The total electromotive force (emf) is the sum of all individual emfs across each component. For example, in a battery with multiple cells in series, each cell's emf adds up to the total voltage output.
  • Same Current: All components share the same current since there is only a single loop for current flow.
Understanding series circuits is crucial when working with batteries, as it helps determine the total voltage provided by the cells.
Lead-Acid Battery
Lead-acid batteries are common rechargeable batteries used in various applications, most notably in automotive vehicles. These batteries work on the principle of electrochemical conversion:
  • Components: Each cell contains lead dioxide (positive plate), sponge lead (negative plate), and a sulfuric acid solution as the electrolyte. When a battery discharges, the chemical reactions work to release electrical energy.
  • Advantages: They are known for providing substantial power in short bursts necessary for starting engines. Lead-acid batteries are economical and reliable for this purpose.
  • Charging and Discharging: During discharge, these batteries convert stored chemical energy into electrical energy, while charging reverses the chemical reactions to store energy once again.
Despite their advantages, one must handle lead-acid batteries with care due to the corrosive nature of the electrolyte and the potential release of hydrogen gas during charging.
Electrical Cells
Electrical cells are the basic building blocks of batteries, converting chemical energy into electrical energy through electrochemical reactions. Each cell consists of three main components:
  • Anode and Cathode: These are the electrodes where reactions occur. The anode releases electrons into the circuit, while the cathode receives electrons.
  • Electrolyte: A substance, often in liquid form or gel, allowing ions to move between the electrodes, facilitating the electrochemical cell reaction.
  • EMF: Each cell possesses an electromotive force (emf), which is the potential difference driving the flow of electrons in the external circuit. The emf of a cell depends on the materials used and the reaction taking place.
In series, multiple electrical cells combine their emfs to increase the total voltage, as seen in lead-acid batteries used in cars, where each cell typically provides an emf of around 2 volts.

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Most popular questions from this chapter

Regarding the units involved in the relationship \(\tau=R C\), verify that the units of resistance times capacitance are time, that is, \(\Omega \cdot \mathrm{F}=\mathrm{s}\)

A \(0.0200-\Omega\) ammeter is placed in series with a \(10.00-\Omega\) resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the \(10.00-\Omega\) resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the \(10.00-\Omega\) resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the \(R C\) constant of the circuit-it is not possible to measure time variations shorter than \(R C\). How would you manipulate \(R\) and \(C\) in the circuit to allow the necessary measurements?

A \(2.00\) - and a \(7.50-\mu \mathrm{F}\) capacitor can be connected in series or parallel, as can a \(25.0\) - and a \(100-\mathrm{k} \Omega\) resistor. Calculate the four \(R C\) time constants possible from connecting the resulting capacitance and resistance in series.

Before World War II, some radios got power through a "resistance cord" that had a significant resistance. Such a resistance cord reduces the voltage to a desired level for the radio's tubes and the like, and it saves the expense of a transformer. Explain why resistance cords become warm and waste energy when the radio is on.
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