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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
Chapter 25, Problem 42

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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First, understand that the power consumed by the cell phone can be calculated using the formula for power: \( P = \frac{E}{t} \), where \( E \) is the energy in joules and \( t \) is the time in seconds.
Convert the time from hours to seconds. Since there are 3600 seconds in an hour, multiply 5.25 hours by 3600 to get the time in seconds.
Substitute the given energy \( E = 3.15 \times 10^4 \) J and the converted time \( t \) into the power formula to find the power \( P \).
Use the relationship between power, voltage, and current: \( P = IV \), where \( I \) is the current and \( V \) is the voltage. Rearrange this formula to solve for the current: \( I = \frac{P}{V} \).
Substitute the calculated power \( P \) and the given voltage \( V = 3.70 \) V into the formula to find the average current \( I \).

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Key Concepts

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

Voltage

Voltage, measured in volts (V), is the electric potential difference between two points. It represents the energy per unit charge available to drive electric current through a circuit. In this problem, the cell phone battery is rated at 3.70 V, indicating the potential energy available to power the device.
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Energy

Energy, measured in joules (J), is the capacity to do work or produce change. Electrical energy is the energy carried by moving electrons in an electric circuit. The battery can produce 3.15 * 10^4 J, which is the total energy available for the phone's operation over a specified period.
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Current

Current, measured in amperes (A), is the rate at which electric charge flows through a conductor. It is calculated by dividing the total energy by the product of voltage and time. In this problem, finding the average current involves using the given energy, voltage, and operational time to determine how much charge flows per second.
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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

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 batteries last for 5.0 h, what is the total energy delivered to the bulb?

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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. The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value?

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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

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

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?