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A voltage source of internal impedance $R_{s}+j X_{s}$ supplies power to a load of impedance $R_{L}+j X_{L}$ in which only $R_{L}$ is variable. Determine the value of $R_{L}$ for maximum power transfer from the source to the load. Also, find the numerical value of $R_{L}$ if the source impedance is $3.0 \; \Omega$ (purely resistive) and $X_{1}$ is $4.0 \; \Omega$.
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