Final answer:
In Physics, for a 50Ω transmission line with SWR of 2, the relation between the real part of the load impedance RL and the imaginary part XL must satisfy the equation RL^2 + (XL ± 25)^2 = 2500.
Step-by-step explanation:
The subject of this question is Physics, specifically dealing with transmission lines and impedance matching. The student is asked to determine the relation between the real part of the load impedance RL and the imaginary part XL for a standing wave ratio (SWR) of 2 on a 50Ω transmission line. The SWR is a measure of impedance mismatch between the transmission line and the load impedance. If the impedance of the load is ZL = RL + jXL, for an SWR of 2 the load impedance along the circle of constant SWR in the Smith chart must satisfy the equation |ZL - Z0| = |Z0 / SWR|, where Z0 is the characteristic impedance of the line (50Ω in this case). Simplifying, this leads to the relation RL^2 + (XL ± Z0/SWR)^2 = Z0^2. Plugging the values in, we get RL^2 + (XL ± 25)^2 = 2500.