Do we get max. power transfer by setting \(Z_S = Z_L\) both in AC and DC circuits?

 

Do we get max. power transfer by setting \(Z_S = Z_L\) both in AC and DC circuits?

For an AC circuit, you get maximum transfer when the load impedance is the COMPLEX CONJUGATE of the source impedance.

 

And for a DC circuit simply when \(Z_L = Z_C\) because there's no phase shift?

 

And for a DC circuit simply when \(Z_L = Z_C\) because there's no phase shift?

that is correct. For a DC circuit, it's pretty easy to prove that maximum power transfer occurs when the load resistance equals the source internal resistance. Rather, I should say, it's easy to demonstrate....while a rigorous mathematical proof is a bit trickier.

If you model a battery as being a voltage source with a fixed value of resistance in series, with a load resistance equal to that value of resistance, you can do a few simple calculations. Calculate what the load's dissipated power would be with a resistance matching that of the battery internal resistance. Now change the value of that load resistance to anything else, and rerun the calculation. You will not find any value that results in MORE power dissipation in the load.

eric