If the gauge number of a wire is increased by $6,$ the diameter is halved; if a gauge number is increased by $1,$ the diameter decreases by the factor $2^{\frac{1}{6}}$. Knowing that $1000 \mathrm{ft}.$ of $10$ gauge copper wire has a resistance of approximately $1.00 \mathrm{\Omega }$. Estimate the resistance of $13 \mathrm{ft}.$ of $22$ gauge copper wire.

Swimming during a storm. The figure, given below, shows a swimmer at distance $D=38.0 \mathrm{m}$ from a lightning strike to the water, with current $I=78 \mathrm{kA}$ . The water has resistivity $30 \mathrm{\Omega m}$ . The width of the swimmer along a radial line from the strike is $0.70 \mathrm{m}$, and his resistance across that width is $4.00 \mathrm{k\Omega }$. Assume that the current spreads through the water over a hemisphere centred on the strike point. What is the current through the swimmer?

Wire $C$ and wire $D$ are made from different materials and have length $L_{\mathrm{C}}=L_{\mathrm{D}}=1.0 \mathrm{m}.$ The resistivity and radius of wire $C$ are $2.0\times {10}^{-6} \mathrm{\Omega m}$ and $1.00 \mathrm{mm},$ and those of wire $D$ are $1.0\times {10}^{-6} \mathrm{\Omega m}$ and $0.50 \mathrm{mm}$. The wires are joined as shown in fig. and a current of $2.0 \mathrm{A}$ is set up in them. What is the electric potential difference between
(a) points $1$ and $2$ and (b) points $2$ and $3$ ? What is the rate at which energy is dissipated between (c) points $1$ and $2$ and (d) points $2$ and $3$?

The current through the battery and resistors $1$ and $2$ in Fig. (a) is $1.50 \mathrm{A}$. Energy is transferred from the current to thermal energy $E_{\mathrm{th}}$ in both resistors. Curves $1$ and $2$ in Fig. (b) give the thermal energy $E_{\mathrm{th}}$ for resistors $1$ and $2,$ respectively, as a function of time $t.$ The vertical scale is set by $E_{\mathrm{th},s}=40.0 \mathrm{mJ},$  and the horizontal scale is set by $t_s=5.00 \mathrm{s}$ . What is the power of the battery?

$\left(\mathrm{a}\right)$  $\left(\mathrm{b}\right)$