Ch 25: Current, Resistance, and EMF

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 25: Current, Resistance, and EMF

Problem 40

Chapter 25, Problem 40

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 V and produce currents of 80 mA (or even larger). A typical pulse lasts for 10 ms. What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?

Verified step by step guidance

First, understand the relationship between voltage (V), current (I), and power (P). Power can be calculated using the formula:

P = V I

. Here, V is the voltage and I is the current.

Substitute the given values into the power formula. The voltage is 500 V and the current is 80 mA. Remember to convert the current from milliamperes to amperes by dividing by 1000:

I = 80 mA = 0.08 A

Calculate the power using the formula:

P = 500 V 0.08 A

. This will give you the power in watts.

Next, calculate the energy delivered during the pulse. Energy (E) can be calculated using the formula:

E = P t

, where t is the time duration of the pulse.

Substitute the power calculated in the previous step and the time duration of the pulse (10 ms, converted to seconds:

10 ms = 0.01 s

) into the energy formula to find the energy delivered in joules.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Power

Electric power is the rate at which electrical energy is transferred by an electric circuit. It is calculated using the formula P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes. Understanding this concept is crucial for determining the power delivered by the electric eel's pulse.

Energy Delivered

Energy delivered in an electrical context is the total work done by the electric current over a period of time. It can be calculated using the formula E = Pt, where E is energy in joules, P is power in watts, and t is time in seconds. This concept helps in calculating the total energy imparted to the enemy during the pulse.

Steady Current

A steady current refers to a constant flow of electric charge over time, without fluctuations. In the context of the electric eel's pulse, assuming a steady current simplifies calculations, as it allows the use of direct formulas for power and energy without needing to account for variations in current or voltage.

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Related Practice

Textbook Question

A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually about 3.0 ms. How much energy is transferred?

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Textbook Question

Consider the circuit of Fig. E25.30. What is the power output of the 16.0 V battery?

Textbook Question

Consider the circuit of Fig. E25.30 Show that the power output of the 16.0 V battery equals the overall rate of consumption of electrical energy in the rest of the circuit.

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Textbook Question

Consider the circuit of Fig. E25.30. At what rate is electrical energy being converted to other forms in the 8.0 V battery?

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Textbook Question

A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. If the internal resistance of the batteries is negligible, what power is delivered to the bulb?

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Textbook Question

The battery for a certain cell phone is rated at 3.70 V. According to the manufacturer, it can produce 3.15 × 10⁴ J of electrical energy, enough for 5.25 h of operation, before needing to be recharged. Find the average current that this cell phone draws when turned on.

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