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(a) During surgery, a current as small as \(20.0 \mu \mathrm{A}\) applied directly to the heart may cause ventricular fibrillation. If the resistance of the exposed heart is \(300 \Omega,\) what is the smallest voltage that poses this danger? (b) Does your answer imply that special electrical safety precautions are needed?

Short Answer

Expert verified
The smallest voltage that poses a risk during surgery with a current of \(20.0 \mu A\) and resistance \(300 \Omega\) is \(6.0 mV\). This small voltage can still have potentially severe consequences when applied directly to the heart, so special electrical safety precautions are necessary during surgery, such as precise monitoring equipment and precautionary measures.

Step by step solution

01

Write down the given information

We are given the following information: - Current \(I = 20.0 \mu A = 20.0 \times 10^{-6} A\) - Resistance \(R = 300 \Omega\) We need to find the smallest voltage \(V\) that poses a risk.
02

Apply Ohm's Law

According to Ohm's Law, the relationship between voltage, current, and resistance is given by the equation: \[V = IR\] Now, we can plug in the given values for current and resistance into the equation to find the smallest voltage \(V\).
03

Calculate the voltage

Insert the values for current and resistance into the equation: \[V = (20.0 \times 10^{-6} A)(300 \Omega)\] Now, calculate the voltage: \[V = (20.0 \times 10^{-6})(300) = 6 \times 10^{-3} V\] So, the smallest voltage that poses a risk is \(V = 6.0 mV\).
04

Assess the need for special electrical safety precautions

A voltage of \(6.0 mV\) is very small; however, given that it can have potentially severe consequences when applied directly to the heart, it's important to take special safety precautions during surgery. This includes using precise monitoring equipment and precautionary measures to prevent any additional or unexpected voltage from being applied to the heart during the procedure, thus reducing the risk of ventricular fibrillation.

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Key Concepts

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

Electrical Safety in Surgery
Understanding electrical safety during surgery is critical, as even low voltages can have significant effects on the human heart. In the context of surgery, the threshold for electrical safety is exceptionally low because the environment and circumstances make the body more vulnerable to current. For instance, a current as small as 20.0 µA if applied directly to the exposed heart, can induce a life-threatening condition known as ventricular fibrillation.

Electrical devices in surgery must adhere to strict safety guidelines to prevent accidental electric shocks. Additionally, operating rooms are equipped with specialized monitoring and electrical insulation to prevent any unintended voltage from reaching the patient. This ensures that the electrical environment remains controlled and below the critical thresholds that can cause harm, such as the calculated 6.0 mV that might trigger ventricular fibrillation.
Ventricular Fibrillation
Ventricular fibrillation (VF) is a severe medical emergency where the heart's ventricles quiver instead of pumping due to disorganized electrical activity. This condition disrupts the heart's ability to effectively pump blood, resulting in a substantial decrease in blood flow to the body's organs.

The onset of VF can be sudden and is often triggered by an electrical disturbance in the heart such as a small voltage applied directly to the heart muscle. In medical contexts, particularly during surgery, the possibility of inducing VF is a critical concern. When the threshold for electrically induced VF is as low as 6.0 mV, it highlights the need for meticulous control of any electrical exposure to the heart and reinforces the use of preventive safety measures in the operating theater.
Resistance and Voltage Relationship
Ohm's Law provides a fundamental principle in understanding the relationship between electrical resistance, voltage, and current. The law, simply stated as V = IR, shows how the voltage (V) across an electrical conductor is proportional to the product of the current (I) flowing through it and its resistance (R).

When considering the medical context, Ohm's Law helps explain why even a small voltage can be dangerous when applied directly to the heart, as seen in the example of the 6.0 mV threshold for ventricular fibrillation. Low resistance in the heart tissue could mean that a correspondingly low voltage is enough to produce a hazardous current. This elucidates the importance of strictly monitoring and regulating the voltage and current that come into contact with the heart during procedures, to ensure that the resistance of the heart does not lead to dangerous levels of electric current.

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