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The relatively high resistivity of dry skin, about 1 × 10^6 ohm.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.

The question aims to find the resistance of the skin of the palm of the hand of an electrical worker whose hand is accidentally touched on a high voltage panel.

The question is based on the concept of resistance of any material. The resistance of any material is defined as the oppositional force exerted by any material to the flow of current through that material. Its formula is given as:

\[ Resistance\ R = \dfrac{ \rho \times Length }{ Area } \]

Here, $\rho$ is called the resistivity of the material, which shows how good any material is in stopping the flow of current.

Expert Answer

The given information for this problem is given as:

\[ Resistivity\ of\ the\ Skin\ \rho = 1.0 \times 10^6 \Omega . m \]

\[ Thickness\ of\ the\ Skin\ t = 1.5 mm \]

To calculate the resistivity of the skin of the hand palm, we need its Area. To calculate the area of the hand, we need the length and breadth of the palm of the hand of the worker. As such information is not given in the question and there is no other way to determine these values. We simply have to assume these values.

Assuming the length of the palm of the hand of an electrical worker is equivalent to the average adult palm, which is given as:

\[ l = 4 in\ or\ 101.6\ mm \]

Similarly, assuming average adult palm breadth for the worker which is given as:

\[ b = 3.3 in\ or\ 83.8\ mm \]

The area of the palm of the hand of the electrical worker is given as:

\[ A = l \times b \]

\[ A = 0.101 \times 0.083 \]

\[ A = 0.0084\ m^2 \]

We can now use the formula of the resistance to calculate the resistance of the skin of the palm, which is given as:

\[ R = \dfrac{ \rho \times t }{ A } \]

Substituting the values, we get:

\[ R = \dfrac{ 1 \times 10^6 \times 1.5 \times 10^{-3} }{ 0.0084 } \]

\[R = 1.8 \times 10^5 \Omega\]

Numerical Result

The area of the skin of the hand that contacted the panel is calculated to be:

\[ A = 0.0084\ m^2 \]

The resistance of the skin of the hand is calculated to be:

\[R = 1.8 \times 10^5 \Omega\]

Example

A worker’s palm touched an electrical panel. The area of the palm is $0.01 m^2$. The resistivity of the skin of the hand is $1 \times 10^6 \Omega.m$. Find the resistance of the skin if the skin is 1 mm thick.

Using the resistance formula to calculate the resistance as:

\[ R = \dfrac{ 1 \times 10^6 \times 1 \times 10^{-3} }{ 0.01 } \]

\[ R = \dfrac{ 1 \times 10^{ 6 – 3 } }{ 0.01 } \]

\[ R = 1 \times 10^5 \Omega\]

The resistance of the skin of the hand of the worker is calculated to be $1 \times 10^5 \Omega$.

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