Question

The relatively high resistivity of dry skin, about 1 × 10⁶ O·m, can safely limit the flow of current into deeper tissues of the body. Suppose an electrical worker places his palm on an instrument whose metal case is accidentally connected to a high voltage. The skin of the palm is about 1.5 mm thick. Estimate the area of skin on the worker’s palm that would contact a flat panel, then calculate the approximate resistance of the skin of the palm.

Answer 1

Area of the flat palm is \(A=\) Length times breadth

$$ \begin{array}{l} =(10 \mathrm{~cm})(15 \mathrm{~cm}) \\ =150 \mathrm{~cm}^{2} \\ =150 \mathrm{~cm}^{2}\left(\frac{10^{-4} \mathrm{~m}^{2}}{1 \mathrm{~cm}^{2}}\right) \\ =1.5 \times 10^{-2} \mathrm{~m}^{2} \end{array} $$

Thickness of skin palm is \(l=1.5 \mathrm{~mm}\)

$$ \begin{aligned} \text { Resistance } R &=\frac{\rho l}{A}=\frac{\left(1.0 \times 10^{6} \Omega \cdot \mathrm{m}\right)\left(1.5 \times 10^{-3} \mathrm{~m}\right)}{1.5 \times 10^{-2} \mathrm{~m}^{2}} \\ &=1.0 \times 10^{5} \Omega \end{aligned} $$