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Electric Eels. Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500 \(\mathrm{V}\) and produce currents of 80 \(\mathrm{mA}\) (or even larger). A typical pulse lasts for 10 \(\mathrm{ms}\) . What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?

Short Answer

Expert verified
The power is 40 W and the energy delivered is 0.4 J.

Step by step solution

01

Understand the given values

We are given that the voltage is \( V = 500 \) V, the current is \( I = 80 \) mA, and the pulse duration is \( t = 10 \) ms. We need to convert the current and time into standard units. - Convert current: \( 80 \text{ mA} = 0.08 \text{ A} \) - Convert time: \( 10 \text{ ms} = 0.01 \text{ s} \)
02

Calculate power using the formula

The formula for power in an electric circuit is given by \( P = V \times I \). Substituting the known values: \[ P = 500 \text{ V} \times 0.08 \text{ A} = 40 \text{ W} \]So, the power delivered is 40 Watts.
03

Calculate energy delivered using power

The energy delivered by the pulse can be calculated using the formula \( E = P \times t \), where \( E \) is energy in joules, \( P \) is power in watts, and \( t \) is time in seconds. Substituting the values we have: \[ E = 40 \text{ W} \times 0.01 \text{ s} = 0.4 \text{ J} \]Thus, the energy delivered to the enemy during each pulse is 0.4 Joules.

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Key Concepts

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

Electric Eels
Electric eels are fascinating creatures, known particularly for their ability to generate electricity. Found predominantly in the murky waters of the Amazon and Orinoco river basins, these unique fish can produce strong electric shocks that serve both as a defensive mechanism and a method of hunting prey. For an electric eel, the ability to generate electricity is vital for stunning prey and defending itself from predators.
  • Electric eels possess specialized cells called "electrocytes."
  • When activated, these cells create an electric current.
  • The head and the tail of the eel become the poles of a battery, resulting in a potent electric field in the water around the eel.
The electric discharge can reach up to 600 volts in some specimens, but the typical example often cited in textbooks is around 500 volts with a current of 80 milliamps. This makes electric eels one of nature's most remarkable examples of self-generated power in the animal kingdom.
Pulse Duration
Pulse duration refers to the length of time over which an electric discharge occurs. For electric eels, a typical pulse is quite short, lasting about 10 milliseconds (ms), a brief span that is enough to stun their prey or scare off potential threats. Understanding pulse duration is crucial because it helps to determine the total energy delivered in each electric shock.

  • The pulse duration is a critical factor in calculating the total energy delivered: shorter pulse durations concentrate energy, thus increasing the intensity of the pulse.
  • The duration of a pulse is directly correlated with its effect; a 10 ms pulse from an electric eel can have a significant impact despite its brevity.
By converting the pulse duration into seconds for calculations (10 ms equals 0.01 seconds), we align the measure with other standard units used in power and energy equations.
Energy Calculation
The calculation of energy in such situations involves understanding how power and time relate to energy. Simply put, energy can be calculated using the formula:\[ E = P \times t \]where \(E\) is energy in joules, \(P\) is power in watts (W), and \(t\) is time in seconds (s). In the case of electric eels, the power is calculated by multiplying the voltage by the current:\[ P = V \times I \]Here, 500 volts (V) and 0.08 amps (A) give us a power of 40 watts (W).

  • Energy delivered by the electric eel's shock is the product of power (40 W) and pulse duration (0.01 seconds), yielding 0.4 joules.
  • Understanding energy calculation is essential for knowing how effective a single pulse is.
This simple yet powerful equation shows how these biological marvels use their built-in energy systems effectively.
Electric Circuits
Electric circuits are paths through which electricity flows. In the context of electric eels, their entire system operates much like a natural electric circuit. Key components include:
  • A source of electrical energy: Electrocytes in the eel function much like the cells of a battery, providing the necessary voltage.
  • The path through which electricity travels: In an eel, this path includes the water around it. Water becomes a medium for the electric current to travel to the prey or predator.
  • Load or output device: While in typical circuits this might be a light bulb or motor, in an eel, it's the stun delivered to the target.
In studying electric circuits, understanding the relationships between voltage, current, and resistance is crucial. The eel's body and environment play roles similar to circuit elements, allowing the eel to direct its electric discharge efficiently. Understanding these concepts enables us to appreciate how the electric eel adapts what is essentially an engineering concept to a biological mechanism, demonstrating the versatility of electric circuits beyond conventional applications.

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Most popular questions from this chapter

The current in a wire varies with time according to the relationship \(I=55 \mathrm{A}-\left(0.65 \mathrm{A} / \mathrm{s}^{2}\right) t^{2}\) . (a) How many coulombs of charge pass a cross section of the wire in the time interval between \(t=0\) and \(t=8.0 \mathrm{s} ?\) (b) What constant current would transport the same charge in the same time interval?

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but they last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100-W incandescent bulb uses only \(23 \mathrm{~W}\) of power. The compact bulb lasts 10,000 hours, on the average, and costs \(\$ 11.00,\) whereas the incandescent bulb costs only \(\$ 0.75,\) but lasts just 750 hours. The study assumed that electricity costs \(\$ 0.080\) per kilowatt-hour and that the bulbs are on for \(4.0 \mathrm{~h}\) per day. (a) What is the total cost (including the price of the bulbs) to run each bulb for 3.0 years? (b) How much do you save over 3.0 years if you use a compact fluorescent bulb instead of an incandescent bulb? (c) What is the resistance of \(\mathrm{a}^{*} 100-\mathrm{W}^{* *}\) fluorescent bulb? (Remember, it actually uses only \(23 \mathrm{~W}\) of power and operates across \(120 \mathrm{~V}\).)

The following measurements were made on a Thyrite resistor: $$\begin{array}{llll}{I(\mathbf{A})} & {0.50} & {1.00} & {2.00} & {4.00} \\\ {V_{a b}(\mathbf{V})} & {2.55} & {3.11} & {3.77} & {4.58}\end{array}$$ (a) Graph \(V_{a b}\) as a function of \(I .(\mathrm{b})\) Does Thyrite obey Ohm's law? How can you tell? (c) Graph the resistance \(R=V_{a b} / I\) as a function of \(I\) .

A person with body resistance between his hands of 10 \(\mathrm{k} \Omega\) accidentally grasps the terminals of a \(14-\mathrm{kV}\) power supply. (a) If the internal resistance of the power supply is \(2000 \Omega,\) what is the current through the person's body? (b) What is the power dissipated in his body? (c) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in the above situation to be 1.00 \(\mathrm{mA}\) or less?

A Nonideal Ammeter. Unlike the idealized ammeter described in Section \(25.4,\) any real ammeter has a nonzero resistance. (a) An ammeter with resistance \(R_{\mathrm{A}}\) is connected in series with a resistor \(R\) and a battery of emf \(\mathcal{E}\) and internal resistance \(r .\) The current measured by the ammeter is \(I_{\mathrm{A}}\) . Find the current through the circuit if the ammeter is removed so that the battery and the resistor form a complete circuit. Express your answer in terms of \(I_{A}, r, R_{\mathrm{A}},\) and \(R .\) The more "ideal" the ammeter, the smaller the difference between this current and the current \(I_{\mathrm{A}}\) . (b) If \(R=3.80 \Omega, \mathcal{E}=7.50 \mathrm{V},\) and \(r=0.45 \Omega,\) find the maximum value of the ammeter resistance \(R_{\mathrm{A}}\) so that \(l_{\mathrm{A}}\) is within 1.0\(\%\) of the current in the circuit when the ammeter is absent. (c) Explain why your answer in part (b) represents a maximum value.

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