(A) Determine the maximum and minimum resistance which can be obtained by joining five resistors of 1/5 Ω each.

The maximum resistance is obtained when resistors are connected in series combination.

Thus \(\displaystyle \mathrm{R}_{\mathrm{S}}=5 \times \frac{1}{5} \Omega=1 \Omega\)

The minimum resistance is obtained when resistors are connected in parallel combination.

\[\begin{aligned} & \frac{1}{\mathrm{R}_{\mathrm{p}}}=\frac{1}{\dfrac{1}{5} \Omega}+\frac{1}{\dfrac{1}{5} \Omega}+\frac{1}{\dfrac{1}{5} \Omega}+\frac{1}{\dfrac{1}{5} \Omega}+\frac{1}{\dfrac{1}{5} \Omega} \\ & \frac{1}{\mathrm{R}_{\mathrm{p}}}=(5+5+5+5+5) \\ & \mathrm{R}_{\mathrm{p}}=\frac{1}{25} \Omega \end{aligned} \]

Heat, \(\displaystyle \mathrm{H}=100 \mathrm{~J}\)

\[\begin{aligned} & \mathrm{R}=4 \Omega \\ & \mathrm{t}=1 \mathrm{~s} \\ & \mathrm{H}=\frac{V^{2} t}{R} \\ & \Rightarrow \mathrm{~V}=\sqrt{\frac{H R}{t}}=\sqrt{\frac{400}{1}}=20 \mathrm{~V} \end{aligned} \]