In a certain system, an electric heating element was found to increase the temperature of a piece of metal $\backslash (10^\{\backslash$circ$\}\backslash )$ for each ampere of current. The metal expands $\backslash (0\mathrm{.}001\backslash$mathrm$\{$~mm$\}/\backslash )$ deg and pushes on a load sensor which outputs $\backslash (1\backslash$mathrm$\{$~V$\}/0\mathrm{.}005\backslash$mathrm$\{$~mm$\}\backslash )$ of compression.

a$.$ Find the transfer functions of the three components and draw the block diagram.

b$.$ Calculate the overall transfer function of this system.