Discussion
A source of angular frequency 1 radian/second has a source impedance consisting of 1 Ω resistance in series with 1 H inductance. The load that will obtain the max power transfer is :
Answer: C
The load is 1 Ω resistance in series with a 1 F capacitor.
Maximum power is transferred when the load impedance is the complex conjugate of the source impedance.
\[ \begin{aligned} Z_{s} &= R + j\omega L = 1 + j(1)(1) = 1 + j1 \\ Z_{L} &= Z_{s}^{*} = 1 - j1 \end{aligned} \]
A reactance of \(-j1\ \Omega\) at \(\omega = 1\) rad/s is a capacitor with \(1/(\omega C) = 1\), so C = 1 F, in series with 1 Ω.
A pure 1 Ω load ignores the source reactance. The parallel combinations give different impedances: 1 Ω in parallel with 1 F, for instance, is \(0.5 - j0.5\ \Omega\), not \(1 - j1\).
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