An ideal transformer has 255 loops in its primary coil and 125 loops in its secondary coil.If the primary current is 2.5 A_rms and the device connected to the secondary uses 100 W of power,what is the rms secondary voltage? A)38.9 V B)19.6 V C)40.0 V D)62.3 V E)100 V

Question

Quizplus · Accepted Answer

First, we need to find the turns ratio of the transformer: 
Np/Ns = 255/125 = 2.04

Next, we can use the power equation: 
P = Vrms^2 / R

Where P = 100 W (power used by the device connected to the secondary), and R is the resistance of the device (which we don't know). However, we can assume that it is purely resistive and use the formula: 
R = Vrms^2 / P

We can also use the turns ratio to relate the primary and secondary voltages: 
Vp / Vs = Np / Ns

Substituting Vp = 2.5 A (primary current) * 255 (number of turns) and Vs = Vrms * 125 (number of turns), we get: 
(2.5*255) / Vrms*125 = 255/125 
Solving for Vrms, we get: 
Vrms = 19.6 V

Therefore, the answer is B.

An Ideal Transformer Has 255 Loops in Its Primary Coil