Question

A person will feel a shock when a current of greater than approximately 100 μA flows between his index finger and thumb.

If the resistance of dry skin is 200 times larger than the resistance of wet skin, how do the maximum voltages without shock compare in each scenario?

A	The voltage on dry skin needs to be 200 times smaller than the voltage on wet skin.
B	The voltage on dry skin needs to be 200 times larger than the voltage on wet skin.
C	The voltage on dry skin is the same as the voltage on wet skin.
D	The voltage on dry skin needs to be 40,000 times larger than the voltage on wet skin.

Answer 1

Concepts and reason This problem is based on the concept of Ohm's Law. The relation between voltage and resistance is to be used to determine the final answer. Ohm's law provides the required relation, which is used to relate the dry skin and wet skin quantities.

Fundamentals

Ohm's Law: The current across an ideal conductor is directly proportional to the potential difference applied across its ends. Write the expression for Ohm's Law. \(V=I R\)

Here, \(I\) is current, \(R\) is resistance, and \(V\) is the potential difference.

Write the expression for Ohm's Law. \(V=I R\)

Here, the current is required \(100 \mu \mathrm{A}\). Since current is constant. \(V \propto R \ldots \ldots\) (1)

Ohm's law is stated, and the relation between voltage and resistance is established, keeping the current constant. The voltage is directly proportional to the resistance.

Equation (1) can be written as:

$$ \frac{V_{1}}{R_{1}}=\frac{V_{2}}{R_{2}} $$

Here \(V_{1}\) is the voltage of wet skin, \(R_{1}\) is the resistance of wet skin, \(R_{2}\) is the resistance of dry skin, and \(V_{2}\) is the voltage of dry skin. Substitute \(200 R_{1}\) for \(R_{2}\) in the above expression.

$$ \begin{array}{l} \frac{V_{1}}{R 1}=\frac{V_{2}}{200 R 1} \\ V_{2}=200 V_{1} \end{array} $$

The relation between wet skin voltage and dry skin voltage is achieved by considering the current constant in Ohm's law.

The voltage on dry skin needs to be 200 times larger than the voltage on wet skin.