A 12.0V ideal battery is connected to resistor R1=6.0Ω in series with a parallel network consisting of a fixed resistor R2=9.0Ω and a variable resistor Rx (whose resistance can be adjusted over a wide range). The connecting wires have negligible resistance.
(a) Derive an algebraic expression for the total current Itot delivered by the battery as a function of the variable resistance Rx.
(b) Determine the value of Rx that results in Itot=2.0A.
(c) For the value of Rx found in part (b), calculate the current through resistor R2.
(d) Discuss qualitatively how the current through resistor R2 changes as Rx is made very large (approaching an open circuit) versus very small (approaching a short circuit). Support your discussion with appropriate reasoning based on circuit principles.