A fixed \(1.0\text{k}\Omega\) resistor and a \(4.0\text{k}\Omega\) potentiometer are connected in series across a 5V battery of negligible internal resistance. Calculate the maximum and minimum values of \(V_{AB}\) based on possible potentiometer settings. (See Subsection 11.5.2 for an explanation of potentiometers.)
Determine an expression for \(V_2\) that results in zero current through resistor \(R_3\text{.}\) Your \(V_2\) expression may only depend on \(V_1\text{,}\)\(R_1\text{,}\)\(R_2\text{,}\)\(R_3\text{,}\)\(R_4\text{,}\) and \(R_5\text{.}\)