Chapter 21, Problem 105PP

BIO Footwear Safety

The American National Standards Institute (ANSI) specifies safety standards for a number of potential workplace hazards. For example, ANSI requires that footwear provide protection against the effects of compression from a static weight, impact from a dropped object, puncture from a sharp tool, and cuts from saws. In addition, to protect against the potentially lethal effects of an electrical shock, ANSI provides standards for the electrical resistance that a person and footwear must offer to the flow of electric current.

Specifically, regulation ANSI Z41-1999 states that the resistance of a person and his or her footwear must be tested with the circuit shown in Figure 21-63. In this circuit, the voltage supplied by the battery is ɛ = 50.0 V and the resistance in the circuit is R = 1.00 MΩ. Initially the circuit is open and no current flows. When a person touches the metal sphere attached to the battery, however, the circuit is closed and a small current flows through the person, the shoes, and back to the battery. The amount of current flowing through the person can be determined by using a voltmeter to measure the voltage drop V across the resistor R. To be safe, the current should not exceed 150 µF.

Notice that the experimental setup in Figure 21-63 is a dc circuit with two resistors in series—the resistance R and the resistance of the person and footwear, R_pf. It follows that the current in the circuit is I = ɛ/(R + R_pf). We also know that the current is I = V/R, where V is the reading of the voltmeter. These relationships can be combined to relate the voltage V to the resistance R_pf with the result shown in Figure 21-64. According to ANSI regulations, Type II footwear must give a resistance R_pf in the range of 0.1 × 10⁷ Ω to 100 × 10⁷ Ω.

Figure 21-63 Problems 103, 104, 105, and 106

105. • The resistance of a given person and footwear is 4.00 × 10⁷ Ω. What is the reading on the voltmeter when this person is tested?

1. A. 0.976 V
2. B. 1.22 V
3. C. 1.25 V
4. D. 50.0 V