A source with an impedance of 100 $\Omega$ is connected to the primary coil of a transformer and a resistance R is connected to the secondary coil. If the transformer has 500 turns in its primary coil and 100 turns in its secondary coil the greatest power will be dissipated in the resistor if R =:
A) 0
B) 0.25$\Omega$
C) 4.0 $\Omega$
D) 50 $\Omega$
E) 100 $\Omega$

Question

Quizplus · Accepted Answer

The impedance seen by the transformer, ZT, is given by ZT = 100 + j0 (since the source has no reactance).
Using the transformer turns ratio, we can find the impedance seen by the resistor, ZR:
ZT/ZR = Np/Ns
(100 + j0)/(R + j0) = 500/100
Simplifying this equation, we get:
R = 4.0 Ω
Now, to maximize power dissipation in the resistor, we want to match the load impedance (i.e. ZR = 4.0 Ω) to the complex conjugate of the source impedance (i.e. ZL = 100 - j0 Ω). This is known as impedance matching.
Therefore, the best choice for R is 4.0 Ω (option C).

A Source with an Impedance of 100 Ω\OmegaΩ Is Connected to the Primary Coil of a Transformer and to the Primary

A Source with an Impedance of 100 $\Omega$ Is Connected to the Primary Coil of a Transformer and to the Primary