Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 50

50 Figure 31-27 shows an “auto-transformer.” It consists of a single coil (with an iron core). Three taps \(T_i\) are provided. Between taps \(T_1\) and \(T_2\) there are 50 turns, and between taps \(T_2\) and \(T_3\) there are 800 turns. Any two taps can be chosen as the primary terminals, and any two taps can be chosen as the secondary terminals. For choices producing a step-up transformer, what are the (a) smallest, (b) second smallest, and (c) largest values of the ratio \(V_s/V_p\)? For a step-down transformer, what are the (d) smallest, (e) second smallest, and (f) largest values of \(V_s/V_p\)?