Problem 45 - University Physics with Modern Physics

Question

Treatment of Heart Failure. 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 \(\mathrm{V}\) for a very short time, usually about 3.0 \(\mathrm{ms}\) . (a) What power does the defibrillator deliver to the body, and (b) how much energy is transferred?

Step-by-Step Solution

Answer

Power is 300 W, and energy transferred is 0.9 J.

Step 1: Understand the Variables

To find the power delivered by the defibrillator, we must clearly understand the variables given: current \( I = 12 \, \mathrm{A} \), voltage \( V = 25 \, \mathrm{V} \), and time \( t = 3.0 \, \mathrm{ms} \). Power \( P \) is defined as the rate of energy transfer. It can be calculated using the formula \( P = IV \).

Step 2: Calculate Power Delivered

Use the formula \( P = IV \) to calculate power.\[P = (12 \, \mathrm{A})(25 \, \mathrm{V}) = 300 \, \mathrm{W}\] Thus, the defibrillator delivers 300 watts of power to the body.

Step 3: Convert Time to Seconds

The time provided is in milliseconds, but we need the time in seconds to calculate energy. Convert milliseconds to seconds:\[t = 3.0 \, \mathrm{ms} = 3.0 \times 10^{-3} \, \mathrm{s}\]

Step 4: Calculate Energy Transferred

Energy transferred \( E \) is the product of power and time. Use the formula \( E = Pt \).\[E = (300 \, \mathrm{W})(3.0 \times 10^{-3} \, \mathrm{s}) = 0.9 \, \mathrm{J}\]Thus, the energy transferred is 0.9 joules.

Key Concepts

Heart Defibrillator

A heart defibrillator is a life-saving device used primarily in emergencies when a person's heart has stopped beating effectively. The main purpose of a defibrillator is to deliver a controlled electric shock to the heart, which can help restore a normal rhythm. This electrical pulse temporarily stops all electrical activity in the heart and gives it a chance to reset. It's like sending a restart command to your computer when it freezes.

These devices are crucial in medical settings and sometimes in public spaces, as they can help prevent sudden cardiac arrest from becoming fatal. They are designed to be easy to use, even for individuals without medical training, due to semi-automated systems that guide the user through the process.

• Typically applies high voltage for a very brief moment.
• Used in scenarios of heart failure or irregular heart rhythms.
• Can be part of automated external defibrillators (AEDs) accessible in public places.

Current and Voltage

In electrical terms, **current** and **voltage** are crucial components for understanding how energy is transferred through a system like a heart defibrillator. Current, denoted as "I" in equations, is the flow of electric charge and is measured in amperes (A). Voltage, represented as "V," is the electric potential difference between two points, measured in volts (V).

For a heart defibrillator, a high current of 12 amperes and a voltage of 25 volts are used to achieve effective energy transfer into the body. This combination ensures that sufficient energy is applied quickly enough to be effective without causing excessive harm or discomfort to the patient. The relationship between current and voltage is critical, as it defines the power output using the equation:

Power Calculation

The power (P) delivered by the defibrillator can be calculated using:

• Formula: \( P = IV \)
• Where \( I = 12 \, \mathrm{A} \) and \( V = 25 \, \mathrm{V} \)
• Resulting in: \( P = 300 \, \mathrm{W} \)

This formula indicates how effectively the device transfers energy at any given moment.

Energy Transfer Calculation

Calculating the energy transferred by a heart defibrillator involves understanding the relationship between power, time, and energy. Energy, in this context, refers to the amount of work done or the amount of electrons moved through an electric circuit, which in the case of a defibrillator, helps the heart muscles reset their contractions.

**Energy Transfer Formula**
To calculate the energy transferred (E) during defibrillation:

• Use the formula: \( E = Pt \)
• Where power \( P = 300 \, \mathrm{W} \) and time \( t = 3.0 \, \mathrm{ms} = 3.0 \times 10^{-3} \, \mathrm{s} \)
• The energy transferred is \( E = 0.9 \, \mathrm{J} \)

By converting milliseconds to seconds, you ensure that the time is correctly factored into the calculation, which deduces the precise amount of energy transmitted during this vital procedure. Understanding this energy transfer is crucial, as applying the correct dosage of energy determines the success of restarting the heart's normal rhythm.