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Chapter 20: Problem 1

A defibrillator is used during a heart attack to restore the heart to its normal beating pattern (see Section 19.5 ). A defibrillator passes 18 A of current through the torso of a person in \(2.0 \mathrm{ms}\). (a) How much charge moves during this time? (b) How many electrons pass through the wires connected to the patient?

Short Answer

Expert verified
(a) 0.036 C of charge moves. (b) Approximately 2.25 x 10^17 electrons pass through.

Step by step solution

01

Define the relationship between current, charge, and time

The relationship between current (\( I \)), charge (\( Q \)), and time (\( t \)) is given by the formula: \\[Q = I \times t\]where \\( Q \)is the charge in coulombs, \\( I \)is the current in amperes, and \\( t \)is the time in seconds. We will use this formula to find the charge.
02

Convert time from milliseconds to seconds

Since the current is given for a time duration in milliseconds, we need to convert \\( t = 2.0 \, \mathrm{ms} \) to seconds. The conversion is: \\[2.0 \, \mathrm{ms} = 2.0 \times 10^{-3} \, \mathrm{s}\]Thus, \\( t = 2.0 \times 10^{-3} \, \mathrm{s} \).
03

Calculate the charge transferred

Substitute the values of current and time into the formula \\( Q = I \times t \). Given \\( I = 18 \, \mathrm{A} \) and \\( t = 2.0 \times 10^{-3} \, \mathrm{s} \), the charge \\( Q \) is calculated as follows: \\[Q = 18 \, \mathrm{A} \times 2.0 \times 10^{-3} \, \mathrm{s} = 0.036 \, \mathrm{C}\]Thus, the charge moved during this time is \\( 0.036 \, \mathrm{C} \).
04

Determine the number of electrons from charge

The charge of a single electron is approximately \\( e = 1.602 \times 10^{-19} \, \mathrm{C} \). To find the number of electrons \\( n \), use the formula: \\[n = \frac{Q}{e}\]Substitute the calculated charge \\( Q = 0.036 \, \mathrm{C} \) and the charge of an electron: \\[n = \frac{0.036 \, \mathrm{C}}{1.602 \times 10^{-19} \, \mathrm{C/e^{-}}} \approx 2.25 \times 10^{17}\]Hence, approximately \\( 2.25 \times 10^{17} \) electrons pass through the wires.

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Key Concepts

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

Electric Current
Electric current represents the flow of electric charge. Think of it as the movement of electric charges within a conductor, like water flowing through a pipe.
Current is measured in amperes (A), which is the standard unit for electric current.

  • In simple terms, one ampere is the flow of one coulomb of charge per second.
  • Electric current usually flows due to the movement of electrons in a conductor.
  • In practical applications like a defibrillator, current is used to deliver electric shocks.
To find current, use the formula: \[ I = \frac{Q}{t} \]Where:
  • \( I \) is the current in amperes
  • \( Q \) is the charge in coulombs
  • \( t \) is the time in seconds
If you know how much charge flows and the time it takes, you can easily determine the current flowing through the circuit.
Electric Charge
Electric charge is a fundamental property of matter, primarily carried by electrons and protons.
It can be positive or negative, influencing how particles interact via electromagnetic forces.

  • A single proton has a positive charge, while a single electron has an equivalent negative charge.
  • The unit of charge is the coulomb (C).
  • Charge conservation means that charge cannot be created or destroyed, only transferred.
In the context of the exercise, charge (\( Q \)) is found by multiplying the current (\( I \)) by the time (\( t \)) the current flows: \[ Q = I \times t \]Using this formula, you can calculate the total charge that moves during a specific time interval, which is particularly useful in medical devices like defibrillators, where the charge restores normal heart rhythm.
Electrons
Electrons are subatomic particles with a negative electric charge. They are fundamental components of atoms, orbiting the nucleus, which contains protons and neutrons.
Electrons play an essential role in electricity as they are the particles that move to generate electric current.

  • The charge of a single electron is approximately \( 1.602 \times 10^{-19} \, \text{C} \).
  • In conductive materials, electrons can move freely, causing an electric current when an electric field is applied.
  • Electrons are responsible for chemical bonding and are vital in the flow of electricity in circuits.
To calculate the number of electrons passing through a conductor, divide the total charge by the charge of a single electron:\[ n = \frac{Q}{e} \]Where:
  • \( n \) is the number of electrons
  • \( Q \) is the total charge in coulombs
  • \( e \) is the charge of one electron
This calculation helps understand how many electrons contribute to the charge transfer in devices like defibrillators, critical in medical emergencies.

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Most popular questions from this chapter

The current in a series circuit is 15.0 A. When an additional \(8.00-\Omega\) resistor is inserted in series, the current drops to \(12.0 \mathrm{A}\). What is the resistance in the original circuit?

A coffee cup heater and a lamp are connected in parallel to the same \(120-\mathrm{V}\) outlet. Together, they use a total of \(111 \mathrm{W}\) of power. The resistance of the heater is \(4.0 \times 10^{2} \Omega .\) Find the resistance of the lamp.

The total current delivered to a number of devices connected in parallel is the sum of the individual currents in each device. Circuit breakers are resettable automatic switches that protect against a dangerously large total current by "opening" to stop the current at a specified safe value. A \(1650-\mathrm{W}\) toaster, a \(1090-\mathrm{W}\) iron, and a \(1250-\mathrm{W}\) microwave oven are turned on in a kitchen. As the drawing shows, they are all connected through a \(20-\mathrm{A}\) circuit breaker (which has negligible resistance) to an ac voltage of \(120 \mathrm{V}\) (a) Find the equivalent resistance of the three devices. (b) Obtain the total current delivered by the source and determine whether the breaker will "open" to prevent an accident.

Two capacitors are connected to a battery. The battery voltage is \(V=60.0 \mathrm{V},\) and the capacitances are \(C_{1}=2.00 \mu \mathrm{F}\) and \(C_{2}=4.00 \mu \mathrm{F}\) Determine the total energy stored by the two capacitors when they are wired (a) in parallel and (b) in series.

In the Arctic, electric socks are useful. A pair of socks uses a \(9.0-\mathrm{V}\) battery pack for each sock. A current of \(0.11 \mathrm{A}\) is drawn from each battery pack by wire woven into the socks. Find the resistance of the wire in one sock.
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