Problem 41 - University Physics with Modern Physics

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. (a) What power does the defibrillator deliver to the body, and (b) how much energy is transferred?

Step-by-Step Solution

Answer

(a) 300 watts, (b) 0.9 joules.

Step 1: Understand the Power Formula

Power is calculated using the formula \( P = IV \), where \( P \) is the power in watts (W), \( I \) is the current in amperes (A), and \( V \) is the voltage in volts (V). Here, given \( I = 12 \) A and \( V = 25 \) V, substitute these values into the formula.

Step 2: Calculate Power Delivered

Using the formula \( P = IV \), substitute \( I = 12 \) A and \( V = 25 \) V into the equation: \( P = 12 \times 25 = 300 \) watts.

Step 3: Understand Energy Formula

Energy transferred is calculated using the formula \( E = Pt \), where \( E \) is energy in joules (J), \( P \) is power in watts, and \( t \) is time in seconds (s). The given time is 3.0 milliseconds, which is 3.0 ms = 3.0 x 10^{-3} s.

Step 4: Calculate Energy Transferred

Substitute \( P = 300 \) W and \( t = 3.0 \times 10^{-3} \) s into the formula \( E = Pt \): \( E = 300 \times 3.0 \times 10^{-3} = 0.9 \) joules.

Key Concepts

Power Calculation

In electrical circuits, calculating power is fundamental when understanding how devices like defibrillators function. The power output of a device is the rate at which it can transfer energy, measured in watts (W). This is crucial for determining how effective the device will be.

A simple and important formula for power calculation is given by \( P = IV \). Here, \( P \) is the power, \( I \) is the current in amperes, and \( V \) is the voltage in volts. In our example with the defibrillator:

• The current \( (I) = 12 \) A
• The voltage \( (V) = 25 \) V

Substituting these values into the formula gives us \( P = 12 \times 25 = 300 \) watts. Therefore, the defibrillator delivers 300 watts of power to the body. Understanding this calculation helps recognize how much energy can be transferred in a given moment, making it critical in life-saving equipment.

Energy Transfer

Energy transfer is a key component in understanding how electrical devices interact with their environment. It tells us how much energy is moved from one system or body to another. In the context of a defibrillator, this is important to assess its effectiveness in restarting a heart.

The formula to calculate energy transferred is \( E = Pt \), where \( E \) is the energy in joules, \( P \) is the power in watts, and \( t \) is the time in seconds during which the power is delivered. The shorter the time, the more precise and immediate the energy transfer.

In our example, we know:

• Power \( P = 300 \) W
• Time \( t = 3.0 \times 10^{-3} \) s (converted from milliseconds)

By substituting into the formula, \( E = 300 \times 3.0 \times 10^{-3} = 0.9 \) joules. So, the defibrillator transfers 0.9 joules of energy to the body in that brief moment.
This brief and potent delivery is essential during an emergency, highlighting the importance of accurate and efficient energy transfer.

Defibrillator Physics

Defibrillators are a fascinating application of physics principles, used to restore a heart's normal rhythm by delivering a controlled electric shock. Understanding how these devices work involves a blend of electricity and human physiology.

These devices operate by delivering a precise amount of power and energy to the heart. The aim is to depolarize the heart muscles, which can potentially reset the normal rhythm of the heart. This requires a delicate balance, as too little energy might be ineffective while too much could cause harm.

Key aspects of defibrillator physics include:

• Current and Voltage: The device needs a high current (12 A in our example) and suitable voltage (25 V) to be effective.
• Time Duration: The energy delivery happens over a very short time span (3 ms in our case), which is critical to avoid harm and achieve the desired reset efficiently.

These calculations and principles ensure that the defibrillator is sufficient for life-saving intervention, highlighting the vital connection between physics and medical technology.