Four separate circuits are constructed, each using the same type of metallic resistor whose resistance remains constant with temperature. In every circuit the resistor is connected directly across an ideal battery. The only difference among the circuits is the emf supplied by the battery, as listed below:
(a) Rank the four circuits from greatest to least steady current. If any circuits have equal current, indicate that clearly.
(b) Provide a concise justification for your ranking based on fundamental principles relating emf, current, and resistance.
(c) Suppose a non-negligible internal resistance r is now present inside each battery, with the same value in every circuit. Derive an expression for the current in terms of ϵ, R, and r, and discuss qualitatively how the inclusion of r might alter the ranking you gave in part (a).