To attain maximum power delivered to a load, what value of load impedance is required if 1. the load can have any complex value; 2. the load must be pure resistance?

Explanation:

Maximum power will be delivered to the load if

Z(load) = Z(t)*

If the Thevenin is defined as Z(t) = R(t) + jX(t), then the load impedance will be

Z(load) = Z(t)* = R(t) - jX(t)

Finding the equivalent impedance, we have that

Z(eq) = Z(t) + Z(load)

Simplifying further, we have

Z(eq) = R(t) + jX(t) + R(t) - jX(t)

Z(eq) = 2R(t)

Therefore, maximum power will be delivered to the load when Z(load) = Z(t)*

Maximum power will be delivered to a pure resistance table if

R(load) = |Z(t)|

Again, if we define the impedance of Thevenin, we have

Z(t) = R(t) + jX(t)

And therefore, our load resistance is

R(load) = √[R(t)² + X(t)²]