91Ó°ÊÓ

Consider the expression for the resistance is:

$$\begin{gathered} R=\frac{V}{I} \\ =\frac{\mathrm{ÒÏ}L}{A} \end{gathered}$$

Here, $\mathrm{ÒÏ}$is resistivity $\mathrm{Î\copyright }·\text{m}$, L is length in A and is area in ${\text{m}}^2$.

Consider the formula for the power dissipated in the circuit.

$P=I^{2}R$ ….. (1)

Consider the given values of resistivity, length and the diameter.

$$\begin{gathered} \mathrm{ÒÏ}=5.0\mathrm{Î\copyright }·\text{m} \\ L=1.6\text{m} \\ d=0.10\text{m} \end{gathered}$$

Substitute the values in resistance formula:

$$\begin{gathered} R=\frac{\mathrm{ÒÏ}L}{A} \\ R=\frac{\mathrm{ÒÏ}L}{\mathrm{Ï€}{\left(\frac{d}{2}\right)}^2} \end{gathered}$$

Substitute the values and solve as:

$$\begin{gathered} R=\frac{\left(5.0\mathrm{Î\copyright }·\text{m}\right)\left(1.6\text{m}\right)}{\mathrm{Ï€}{\left(\frac{0.10}{2}\right)}^2} \\ =1019\mathrm{Î\copyright } \end{gathered}$$

Hence, the resistance between the hands if the skin resistance is negligible is $1019\mathrm{Î\copyright }$.

(b)

Consider the value of the current.

$I=100\text{mA}$

Consider the expression value of the voltage from the Ohm’s law.

$$\begin{gathered} V=\left(100\text{mA}\right)\left(1019\mathrm{Î\copyright }\right) \\ =102\text{V} \end{gathered}$$

Hence, the potential difference between the hands is needed for a lethal shock current of $100\text{mA}$is 102 V .

(c)

Consider the value of the current.

$I=100\text{mA}$

Substitute the values in the equation (1) to determine the power.

$$\begin{gathered} P={\left(100\text{mA}\right)}^2\left(1019\mathrm{Î\copyright }\right) \\ =10.19\text{W} \end{gathered}$$

Hence, power is dissipated in the body.