Q$2-(25$ pts$)$ A variable resistor, $\backslash ($ R $\backslash ),$ whose value ranges from $0$ to $\backslash (\backslash$infty $\backslash )$ is connected between the terminals of a battery that has an emf $\backslash (\backslash$varepsilon$=\backslash )18\mathrm{.}0$ V $,$ and an internal resistance of $\backslash (4\mathrm{.}00\backslash$Omega $\backslash ).$ The ammeter and voltmeter are idealized meters.

a$)(8$ pts$.)$ As $\backslash ($ R $\backslash )$ varies over its full range of values, what will be the largest and smallest readings of the voltmeter and ammeter? Justify each answer with statement and$/$or direct calculation below.

b$)(8$ pts$.)$ The power dissipated at the variable resistor is $18\mathrm{.}0$ W $.$ What can be the maximum reading on the voltmeter in this case?

c$)(9$ pts$.)$ Suppose we replace the variable resistor with a cylindrical wire of length $8\mathrm{.}0$ cm and cross section diameter $0\mathrm{.}5$ cm $.$ The voltmeter reads $15\mathrm{.}0$ V $.$ Calculate resistivity of the cylindrical wire, the magnitudes of the current density and the electric field through the wire.