 So I've done this so far, and know one of the components is a 50ohm resistor. However I dont know where to go from here. How do i decide if its an inductor or a capacitor?
This is a past paper exam so im aware the other component is a 125nH inductor... but how do i get to that?

• Are you sure about all of that? My intuition would be that you want the the mystery load to have a resistance equal to RL for max power transfer, and a reactive component that cancels out the impedance of CL at source's frequency (i.e. resonance) which means it can only be an inductor whose impedance is equal but opposite to that of CL at the source frequency. Which is 100nH. – DKNguyen May 21 at 22:14
• $\omega C=1/(\omega L)$ and L is in parallel with 10 Ohms. – Tony Stewart Sunnyskyguy EE75 May 21 at 22:20
• Possible duplicate of Maximum power transfer theorem – Elliot Alderson May 21 at 22:50

$$\Z_L=10+\frac{1}{j\omega C}\$$ turns out 10+j20, well it can't. $$\\frac{1}{j\omega C} = \frac{-j}{\omega C}\$$ , so it has to be negative. On the source side the conjugate complex would give a positive imaginary number, so an inductor.
$$Z_L=R_L+\frac{1}{j\omega C_L}=R_L-\frac{j}{\omega C_L}$$ $$Z_L={Z_S}^*$$ $$Z_S=R_L-\frac{1}{j\omega C_L}=R_L+\frac{j}{\omega C_L}$$ $$Z_S=R_S+j\omega L_S$$ $$R_S=R_L , \ \omega L_S=\frac{1}{\omega C_L}$$