Question

Consider a step-down transformer with 15 turns in the primary and 6 turns in the secondary windings. Calculate the input impedance of this transformer loaded to an 8 Ω resistor, assuming that series resistances of the windings are negligible.

Answer 1

Answer:

Input impedance of this transformer is 50 ohms.  

Explanation:

Given that,

Number of turns in the primary coil, $N_p=15$

Number of turns in the secondary coil, $N_s=6$

Output impedance of the transformer, $V_o=8\ \Omega$

The number of turns and the impedance ratio in the step down transformer is given by :

$\dfrac{15}{6}=\sqrt{\dfrac{Z_p}{Z_s}}\\\\\dfrac{15}{6}=\sqrt{\dfrac{Z_p}{8}}\\\\Z_p=50\ \Omega$

So, the input impedance of this transformer is 50 ohms. Hence, this is the required solution.