Problem 14 - Fundamentals of Physics

Question

A human being can be electrocuted if a current as small as 50 mA passes near the heart. An electrician working with sweaty hands makes good contact with the two conductors he is holding, one in each hand. If his resistance is \(2000 \Omega,\) what might the fatal voltage be?

Step-by-Step Solution

Answer

The fatal voltage could be 100 V.

Step 1: Identify the known quantities

The problem gives the following information: the minimum current that can cause electrocution is 50 mA (0.05 A) and the electrician's resistance is 2000 Ohms.

Step 2: Recall Ohm’s Law

Ohm’s Law is expressed by the formula \( V = I \times R \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance.

Step 3: Substitute the known values into Ohm's Law

Using Ohm's law, substitute the known values: \( I = 0.05 \text{ A} \) and \( R = 2000 \Omega \) into the formula \( V = I \times R \). So, \( V = 0.05 \times 2000 \).

Step 4: Calculate the voltage

Multiply the current (0.05 A) by the resistance (2000 Ohms) to find the voltage: \( V = 0.05 \times 2000 = 100 \text{ V} \).

Key Concepts

Electrocution

Electrocution is a serious risk that occurs when an electric current passes through the human body, potentially causing injury or even death. Understanding the dangers of electrocution can help in prevention and safety measures. The harm caused by electrocution depends primarily on:

• Amount of Current: The severity is directly tied to the amount of current that flows through the body. As little as 50 milliamperes (mA) can be enough for electrocution, especially if it passes near vital organs like the heart.
• Path of Current: The pathway that the electric current takes through the body is crucial. Current passing through vital organs such as the heart is more likely to be fatal.
• Duration of Exposure: Longer exposure increases the severity of electrocution. Quick reflexes and circuit breakers are essential in preventing prolonged exposure.

By recognizing these factors, staying safe around electricity becomes more manageable. Using proper insulation, avoiding contact with water while dealing with electrical systems, and wearing protective gear are all crucial steps in reducing electrocution risks.

Resistance

Resistance is a measure of how much a material opposes the flow of an electric current. It is an important concept in understanding how electrical systems work, including the human body's interaction with electricity. The unit of resistance is the ohm (Ω).

• Body Resistance: The human body naturally has a certain resistance to electrical flow. This resistance can vary depending on factors such as moisture on the skin, with sweaty or wet skin significantly lowering resistance.
• Material Conductivity: Good conductors like metals have low resistance, making them carry electric current easily, whereas insulators like rubber have high resistance.
• Role in Safety: Knowing the resistance of different materials helps in designing safe electrical systems, ensuring that the current stays within safe limits to prevent damage and hazards.

A basic understanding of resistance in materials and the human body is fundamental for applying safety principles when working with electricity.

Voltage Calculation

Voltage calculation is an essential skill for anyone working with electrical systems. It involves determining the amount of electric potential, or voltage, in a circuit. For example, consider the situation in the exercise where we calculate the fatal voltage for an electrician using Ohm's Law.
Ohm's Law is expressed as \( V = I \times R \), where:

• \( V \) (Voltage): The potential difference we want to find, measured in volts.
• \( I \) (Current): The electric current flowing through the circuit, in amperes.
• \( R \) (Resistance): The opposition of current flow measured in ohms.

Using the exercise parameters: the current (\( I \)) is 0.05 A and the resistance (\( R \)) is \(2000 \Omega\). By substituting into Ohm's Law, the fatal voltage: \[ V = 0.05 \times 2000 = 100 \text{ V} \]This calculation highlights the importance of knowing resistance and current to ensure electric circuits are safe and functional.