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Chapter 18: Problem 25

A person can be killed if a current as small as \(50 \mathrm{mA}\) passes near the heart. An electrician is working on a humid day with hands damp from perspiration. Suppose his resistance from one hand to the other is $1 \mathrm{k} \Omega$ and he is touching two wires, one with each hand. (a) What potential difference between the two wires would cause a 50 -mA current from one hand to the other? (b) An electrician working on a "live" circuit keeps one hand behind his or her back. Why?

Short Answer

Expert verified
Answer: The potential difference between the two wires that would cause a 50 mA current from one hand to the other is 50 volts. An electrician keeps one hand behind their back when working on live circuits to prevent the risk of creating a closed-loop circuit through their body, which could cause the flow of current across their chest or through their heart, leading to potentially dangerous or life-threatening situations.

Step by step solution

01

Convert given quantities to standard units

First, let's convert the dangerous current level and resistance to standard units: - Given current: 50 mA, which is equal to \(50 * 10^{-3} A\) (since 1 mA = 0.001 A) - Given resistance: 1 kΩ, which is equal to \(1000 \Omega\) (since 1 kΩ = 1000 Ω) Now, we have the current (I) and resistance (R) in standard units.
02

Calculate potential difference using Ohm's Law

Ohm's law states that \(V = IR\). We can substitute the values of the given dangerous current (I) and the electrician's resistance (R) to find the potential difference (V) required to generate the dangerous current. \(V = IR = (50 * 10^{-3} A) * (1000 \Omega)\)
03

Simplify the expression and find the potential difference

Now, we'll simplify the expression: \(V = (50 * 10^{-3}) * 1000\) \(V = 50\) So, the potential difference between the two wires that would cause a 50 mA current from one hand to the other is 50 volts.
04

Explain why an electrician keeps one hand behind the back when working on live circuits

An electrician keeps one hand behind their back when working on live circuits to avoid the possibility of creating a closed-loop circuit throughout their body by accidentally touching two live wires simultaneously with both hands. By keeping one hand behind the back, they prevent the flow of current across their chest or through the heart, which significantly reduces the risk of a potentially dangerous or life-threatening situation

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Most popular questions from this chapter

Two electrodes are placed in a calcium chloride solution and a potential difference is maintained between them. If $3.8 \times 10^{16} \mathrm{Ca}^{2+}\( ions and \)6.2 \times 10^{16} \mathrm{Cl}^{-}$ ions per second move in opposite directions through an imaginary area between the electrodes, what is the current in the solution?
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