Transformers — Question 8

Question 8

Secondary polarity controls whether series voltages add or subtract

Two isolated secondary windings on the same ideal core have 40 and 60 turns. The induced rms voltage is .500 V per turn. Their dotted-to-undotted voltages are in phase.

1. Find the voltage across the free terminals when the undotted end of winding 1 is joined to the dotted end of winding 2.

2. Find the magnitude when the two undotted ends are instead joined, and explain the difference.

Question 8 - Solution

Secondary polarity controls whether series voltages add or subtract

(a) Method and calculation

$$V_1=(40)(.500)=20.0\,V,\quad V_2=(60)(.500)=30.0\,V.$$$$\boxed{V_{\mathrm{aiding}}=V_1+V_2=50.0\,V}.$$

(b) Interpretation and further calculation

$$V_{d1}-V_{d2}=V_1-V_2\quad\text{when undotted ends are common}.$$$$\boxed{|V_{\mathrm{opposing}}|=|20-30|=10.0\,V}.$$

Physical check

Turn counts determine magnitudes; winding polarity determines the sign in the terminal sum.