Problem 36 - College 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

(a) 300 W; (b) 0.9 J.

Step 1: Understanding the Problem

We need to find the power delivered by the defibrillator and the energy transferred to the body. Power is the rate of energy transfer per unit time, and energy can be found by multiplying power by time.

Step 2: Calculating the Power Delivered

Power can be calculated using the formula \( P = IV \), where \( I \) is the current and \( V \) is the voltage. Given \( I = 12 \) A and \( V = 25 \) V, we have:\[P = 12 \, \text{A} \times 25 \, \text{V} = 300 \, \text{W}\]So, the power delivered by the defibrillator is 300 watts.

Step 3: Calculating the Energy Transferred

Energy transferred can be found by multiplying the power by the time during which the current is flowing. The time given is 3.0 ms, which we convert to seconds: \( 3.0 \, \text{ms} = 0.003 \, \text{s} \). Thus, using the formula \( E = Pt \), we have:\[E = 300 \, \text{W} \times 0.003 \, \text{s} = 0.9 \, \text{J}\]Therefore, the energy transferred is 0.9 joules.

Key Concepts

Power Calculation

When dealing with a defibrillator, the power calculation is crucial to understand how much "work" or energy conversion occurs per unit of time. Power (\( P \)) is calculated using the formula:

• \( P = IV \)
• \( I \) is the current in amperes (A)
• \( V \) is the voltage in volts (V)

The rate at which electrical power is delivered tells us how quickly energy is being used. In the case of a defibrillator:- The current \( I \) is 12 A- The voltage \( V \) is 25 V
Substituting these values into the formula gives us:\[ P = 12 \, \text{A} \times 25 \, \text{V} = 300 \, \text{W} \]This means the defibrillator delivers 300 watts of power to the body. This high power level, even if for a short time, enables the defibrillator to perform its function effectively.

Energy Transfer

Energy transfer in physics describes how energy moves from one system to another. In the context of the defibrillator exercise, energy transfer tells us how much energy is actually being deposited into the body during the defibrillation process. To calculate this, you need to know:

• Power (\( P \)), the rate of energy transfer
• The duration of time (\( t \)) for which the power is delivered

The energy transferred (\( E \)) is given by the equation:\[ E = Pt \]Where time must be in seconds for consistency with watts and joules. In the exercise:- The power is 300 W- The time is given as 3.0 ms, which is 0.003 s
Substituting these into the formula:\[ E = 300 \, \text{W} \times 0.003 \, \text{s} = 0.9 \, \text{J} \]Thus, 0.9 joules of energy is transferred to the body. This precise energy transfer is critical for the effective operation of a defibrillator, ensuring just enough energy is provided to achieve the desired outcome.

Electrical Current

Electrical current is a key concept in understanding how defibrillators work. Current is the flow of electric charge, measured in amperes (A). It signifies how much electric charge is passing through a particular area per unit time. There are essential factors to remember about current when considering defibrillators:

• A higher current means more charges are flowing, which can lead to more energy transfer if the voltage is constant.
• For a defibrillator, a large current is essential for effectiveness, as it helps to restart the heart's rhythm.

In the context of the exercise, the defibrillator uses a current of 12 A. This robust current delivers a strong enough impulse to the heart muscles: - Adequate to stimulate heart contractions - Sufficient to reset the electrical pathways in cardiac muscles
Understanding electrical current in this manner aids in comprehending how defibrillators provide an immediate, albeit temporary, electrical reset necessary to attempt restarting the heart.