A matching transformer's primary needs______ more turns than its secondary to match a 600 $\Omega$ audio signal distribution line to an 8$\Omega$ speaker.
A) 0.013
B) 8.66
C) 75
D) 0.115

Question

A matching transformer's primary needs______ more turns than its secondary to match a 600 $\Omega$ audio signal distribution line to an  8$\Omega$ speaker.
A)  0.013 
B)  8.66 
C) 75
D)  0.115

Quizplus · Accepted Answer

The turns ratio required to match the 600 $\Omega$ line to the 8$\Omega$ speaker can be calculated as follows:

\begin{equation}
\frac{N_p}{N_s} = \sqrt{\frac{Z_p}{Z_s}} = \sqrt{\frac{600}{8}} = 12.25
\end{equation}

Therefore, the primary needs 12.25 times more turns than the secondary. Since the turns ratio is a ratio of primary turns to secondary turns, we can simplify this by dividing both sides by the larger number (primary turns) to get:

\begin{equation}
\frac{N_s}{N_p} = \frac{1}{12.25} = 0.0816...
\end{equation}

We can round this to 0.082 or 1:12.25. This means that for every 12.25 turns on the primary, we need one turn on the secondary.

Note that none of the answer choices match this exactly, but choice B, 8.66, is the closest. This is because:

\begin{equation}
\frac{1}{12.25} \approx \frac{1}{8.66}
\end{equation}

Therefore, the best choice is B: 8.66.

A Matching Transformer's Primary Needs______ More Turns Than Its Secondary Ω\OmegaΩ

A Matching Transformer's Primary Needs______ More Turns Than Its Secondary $\Omega$