The figure shows an \"autotransformer.\" It consists of a single coil (with an i

Question

The figure shows an "autotransformer." It consists of a single coil (with an iron core). Three taps Ti are provided. Between taps T1 and T2 there are 217 turns, and between taps T2 and T3 there are 823 tums. 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 rati V ? For a step down trans ormer hat are the small e eco a smallest and (f) largest values of Vs/Vp? Ti (a) Number (b) Number (c) Number Units Units Units (d) Number (e) Number (f) Number Units Units Units

Explanation / Answer

For step-up transformer:

(a)

The smallest value of the ratio /Vs/ Vp is achieved by using T2T3 as primary and T1T3 as secondary coil:

V13/V23 = (823 + 217)/823 = 1.264

(b)

The second smallest value of the ratio Vs/ Vp is achieved by using T1T2 as primary and T2T3 as secondary coil:

V23/V13 = 823/217 = 3.79

(c)

The largest value of the ratio Vs/ Vp is achieved by using T1T2 as primary and T1T3 as secondary coil:

V13/V12 = (823 +217)/217 = 4.79

(d)

The smallest value of the ratio Vs/ Vp is 1/4.79 = 0.209

(e)

The second smallest value of the ratio Vs/Vp is 1/3.79 = 0.264

(f)

The largest value of the ratio Vs/ Vp is 1/1.264 = 0.79

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