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Foolishly trying to fish a burning piece of bread from a toaster with a metal butter knife, a man comes into contact with 120-V AC. He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path the current follows through the person?

a) 2400 Ω
b) 4800 Ω
c) 3600 Ω
d) 1200 Ω

1 Answer

6 votes

Final answer:

None of the provided options are correct. The minimum resistance that would lead to no perception of shock from a 120-V AC source is 120 kΩ, which is higher than all the options provided.

Step-by-step explanation:

The question is regarding the electrical safety related to the human body's resistance when exposed to a voltage source. A man, while trying to fish a piece of bread from a toaster with a metal butter knife, comes into contact with a 120-V AC source but feels no shock because he is wearing rubber-soled shoes, which are good electrical insulators. To find the minimum resistance of the current path through the human body that resulted in no sensation of the electrical shock, standard electrical safety guidelines suggest the perception threshold for current is typically around 1 mA for AC.

Using Ohm's Law (V = IR), where V is voltage (120 V), I is current (1 mA = 0.001 A for the perception threshold), and R is resistance, we can calculate the minimum resistance (R) as follows:
R = V / I = 120 V / 0.001 A = 120,000 Ω (Ohms).

The minimum resistance would be 120 kΩ, which is significantly higher than all the options provided in the multiple-choice question. Hence, none of the options (a) 2400 Ω, (b) 4800 Ω, (c) 3600 Ω, or (d) 1200 Ω are correct, as they are all less than 120 kΩ. A resistance of at least 120 kΩ is required to limit the current to a non-perceptible level below the perception threshold.

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