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Chapter 5: Problem 18

BI0 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
Power: 40 W; Energy: 0.4 J.

Step by step solution

01

Calculate Power

Power (P) in an electric circuit can be calculated using the formula \(P = V \times I\), where \(V\) is the voltage and \(I\) is the current. Given \(V = 500 \mathrm{~V}\) and \(I = 80 \mathrm{~mA}\ = 0.080 \mathrm{~A}\), we find:\[ P = 500 \mathrm{~V} \times 0.080 \mathrm{~A} = 40 \mathrm{~W} \]Thus, the power delivered by the eel is \(40\) watts.
02

Calculate Energy

Energy can be calculated by multiplying power by time. The formula is \(E = P \times t\), where \(E\) is energy, \(P\) is power, and \(t\) is time. The pulse lasts for \(10\) milliseconds, which is \(10 \times 10^{-3}\) seconds. Therefore:\[ E = 40 \mathrm{~W} \times 10 \times 10^{-3} \mathrm{~s} = 0.4 \mathrm{~J} \]Thus, the energy delivered by a single 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 Circuits
Electric circuits form the foundation for understanding how electric power and energy are transferred. They are pathways made up of different electrical components that create a closed loop for electric current to flow. Imagine electric circuits as roads where electricity travels. These roads can have various components such as resistors, capacitors, and power sources, each influencing how electricity is managed.

In the context of electric eels, imagine their body as a unique kind of electric circuit. The eels have specialized cells called electrocytes that work together like series and parallel components in a circuit. This arrangement allows them to generate powerful electrical pulses, similar to flipping a switch that releases current through a circuit. These pulses can deliver significant power, enough to stun prey or enemies, showcasing just how effective natural electric circuits can be.
Current and Voltage
Current and voltage are the dynamic duo in understanding electric circuits. Think of current as the flow of electric charge, similar to how water flows through a pipe. The more electric charge flowing, the higher the current. Current is measured in amperes (A). In our electric eel scenario, the current reaches up to 80 mA or 0.080 A.

Next is voltage, which is akin to the pressure pushing the current through the circuit, similar to water pressure pushing water. Voltage is measured in volts (V), and for electric eels, this can be up to 500 V. The combination of these two factors determines how powerful an electric pulse can be.
  • **Current (I)**: Flow of electric charge. Measured in amperes.
  • **Voltage (V)**: Electric potential difference. Measured in volts.
Each of these components plays a crucial role in delivering power when the eel releases its electric pulse.
Energy Calculations
Understanding energy calculations requires a grasp of how power relates to energy over time. Power, measured in watts (W), is the rate at which energy is transferred or converted. To find energy, we multiply power by time.

For electric eels, the power of a pulse is determined using the formula \(P = V \times I\). Here, with a voltage of 500 V and a current of 0.080 A, the power is 40 W. This power, when applied over the duration of the pulse鈥�10 milliseconds or 10 x 10鈦宦� seconds鈥攄elivers energy. Using the formula \(E = P \times t\), we calculate that 0.4 joules of energy are delivered with each pulse.
  • **Power (P)**: Product of voltage and current. Measured in watts.
  • **Energy (E)**: Product of power and time. Measured in joules.
These calculations illustrate how electric eels can effectively utilize short, intense bursts of electricity.

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Most popular questions from this chapter

A 1.50-m cylindrical rod of diameter \(0.500 \mathrm{~cm}\) is connected to a power supply that maintains a constant potential difference of \(15.0 \mathrm{~V}\) across its ends, while an ammeter measures the current through it. You observe that at room temperature \(\left(20.0^{\circ} \mathrm{C}\right.\) ) the ammeter reads \(18 \mathrm{~A}\), while at \(90.0^{\circ} \mathrm{C}\) it reads \(16.5 \mathrm{~A}\). You can ignore any thermal expansion of the rod. Find (a) the resistivity at \(20.0^{\circ} \mathrm{C}\) and (b) the temperature coefficient of resistivity at \(20^{\circ} \mathrm{C}\) for the material of the rod.

Light Bulbs. The power rating of a light bulb (such as a \(100-W\) bulb) is the power it dissipates when connected across a \(120-\mathrm{V}\) potential difference. What is the resistance of (a) a 100-W bulb and (b) a 60-W bulb? (c) How much current does each bulb draw in normal use?

The potential difference across the terminals of a battery is \(8.40 \mathrm{~V}\) when there is a current of \(1.50 \mathrm{~A}\) in the battery from the negative to the positive terminal. When the current is \(3.50 \mathrm{~A}\) in the reverse direction, the potential difference becomes \(9.4 \mathrm{~V}\). (a) What is the internal resistance of the battery? (b) What is the emf of the battery?

A silver wire \(2 \mathrm{~mm}\) in diameter transfers a charge of \(420 \mathrm{C}\) in \(70 \mathrm{~min}\). Silver contains \(6 \times 10^{2 \mathrm{~g}}\) free electrons per cubic meter. (a) What is the current in the wire? (b) What is the magnitude of the drift velocity of the electrons in the wire?

A resistor with resistance \(R\) is connected to a battery that has emf \(12.0 \mathrm{~V}\) and internal resistance \(r=0.40 \Omega .\) For what two values of \(R\) will the power dissipated in the resistor be \(80.0 \mathrm{~W}\) ?
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