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Chapter 21: Problem 24

(a) Many battery-operated devices take more than one battery. If you look closely in the battery compartment, you will see that the batteries are wired in series. Consider a flashlight circuit. What does the loop rule tell you about the effect of putting several batteries in series in this way? (b) The cells of an electric eel's nervous system are not that different from ours - each cell can develop a voltage difference across it of somewhere on the order of one volt. How, then, do you think an electric eel can create voltages of thousands of volts between different parts of its body?

Short Answer

Expert verified
(a) Batteries in series add their voltages. (b) Electric eels line up cells that add their voltages in series.

Step by step solution

01

Understanding Batteries in Series

When batteries are connected in series, the total voltage of the series is the sum of the voltages of each individual battery. This is because in a series circuit, the loop rule states that the total voltage across any closed loop in a circuit is zero. Therefore, as you move around the loop, the sum of the potential increases provided by the batteries must equal the sum of the potential drops across the rest of the loop. Thus, the more batteries you add in series, the higher the total voltage.
02

Analyzing the Loop Rule in a Flashlight

Applying this principle to a flashlight, when you insert multiple batteries in series, the total voltage that powers the bulb is increased. Each battery adds to the total potential difference available in the circuit, allowing the flashlight to have a stronger and brighter output as the potential differences add up according to the loop rule.
03

Understanding Electric Eel's Voltage Generation

An electric eel generates high voltages by aligning many cells in series. Each cell of the eel acts like a small battery, with each producing about one volt. By connecting thousands of these cells in series, the voltages add up to reach thousands of volts. This is similar to adding multiple batteries in series: each contributes its voltage to reach a higher total voltage.
04

Conclusion on Voltage Accumulation

Thus, both in the flashlight and electric eel, when components (either batteries or cells) are connected in series, their voltages add together. This series arrangement is essential for achieving high voltages from multiple lower voltage components.

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Key Concepts

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

Batteries in Series
When you connect batteries in series, you're essentially stacking their voltages on top of each other. This is like putting together the strength of each battery to make one strong battery. Imagine each battery as a step on a staircase. When you stack the steps, each adds to the height you can reach.
  • Each battery contributes its voltage to the total.
  • The combined voltage is the sum of all individual voltages.
  • This setup is common in devices like flashlights to provide enough power.
Understanding this concept is crucial as it allows for designing circuits that need a specific voltage to operate. With more batteries, you can power devices requiring higher energies.
Loop Rule
The loop rule is a fundamental law in circuits. It states that the total voltage around any closed loop in a circuit must be zero. This happens because the potential increases and decreases in a loop must balance out. Think of it like a budget: if you spend a certain amount, you must balance it out by the end of the cycle.
In a flashlight with batteries in series:
  • Each battery contributes to the energy pushing through the circuit.
  • The sum of voltages from the batteries equals the sum of voltage drops in the rest of the loop.
  • This ensures that all energy provided by the batteries efficiently powers devices.
Using the loop rule helps in understanding how energy flows and is distributed in electrical circuits.
Voltage Generation
Voltage generation is the process of creating electric potential. Consider it like building pressure in a water pipe. More pressure moves water further; similarly, more voltage moves electric charge further.
Ways to generate electrical voltage include:
  • Chemical reactions in batteries.
  • Mechanical means, like generators.
  • Biological processes, as seen in electric eels.
Generating voltage is crucial in powering devices and enables us to convert various forms of energy into usable electrical energy, providing power to countless applications.
Electric Eel
Electric eels are intriguing creatures capable of generating substantial electric voltages. Each tiny nerve cell of an eel produces about one volt, like a small battery. By aligning thousands of these cells in series, the electric eel creates powerful electric fields.
Key points to understand about electric eel voltage generation:
  • Each cell functions similarly to a battery by maintaining a voltage difference.
  • The series arrangement multiplies the voltage, mirroring battery setups in circuits.
  • This enables the eel to both sense its environment and stun prey.
Electric eels exemplify nature's unique method of voltage generation, inspiring technological advancements in bioelectric devices.

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Most popular questions from this chapter

A person in a rural area who has no electricity runs an extremely long extension cord to a friend's house down the road so she can run an electric light. The cord is so long that its resistance, \(x\), is not negligible. Show that the lamp's brightness is greatest if its resistance, \(y\), is equal to \(x\). Explain physically why the lamp is dim for values of \(y\) that are too small or too large.

(a) Express the power dissipated by a resistor in terms of \(R\) and \(\Delta V\) only, eliminating \(I\). (b) Electrical receptacles in your home are mostly \(110 \mathrm{~V}\), but circuits for electric stoves, air conditioners, and washers and driers are usually \(220 \mathrm{~V}\). The two types of circuits have differently shaped receptacles. Suppose you rewire the plug of a drier so that it can be plugged in to a \(110 \mathrm{~V}\) receptacle. The resistor that forms the heating element of the drier would normally draw \(200 \mathrm{~W}\). How much power does it actually draw now?

(a) You take an LP record out of its sleeve, and it acquires a static charge of \(1 \mathrm{nC}\). You play it at the normal speed of \(33 \frac{1}{3}\) r.p.m. and the charge moving in a circle creates an electric current. What is the current, in amperes? (b) Although the planetary model of the atom can be made to work with any value for the radius of the electrons' orbits, more advanced models that we will study later in this course predict definite radii. If the electron is imagined as circling around the proton at a speed of \(2.2 \times 10^{6} \mathrm{~m} / \mathrm{s}\), in an orbit with a radius of \(0.05 \mathrm{~nm}\), what electric current is created? The charge of an electron is \(-e=-1.60 \times\) \(10^{-19} \mathrm{C}\)

You have to do different things with a circuit to measure current than to measure a voltage difference. Which would be more practical for a printed circuit board, in which the wires are actually strips of metal embedded inside the board? \(\quad \triangleright\) Solution, p. 1032

How many different resistance values can be created by combining three unequal resistors? (Don't count possibilities where not all the resistors are used.)
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