Final answer:
The characteristic impedance of the transmission line is calculated using the input impedance and the load impedance. For a quarter-wavelength transmission line terminated with a 300-ohm load and having an input impedance of 75 ohms, the characteristic impedance is found to be 150 ohms.
Step-by-step explanation:
The question is centered on the concept of transmission lines in electrical engineering, a topic often covered in advanced high school physics courses. When a transmission line is terminated with a load, its input impedance can be calculated using the characteristic impedance of the line and the load impedance. The formula for the input impedance Zin of a quarter-wavelength (λ/4) transmission line is:
Zin = (Z0^2) / ZL
where Z0 is the characteristic impedance, and ZL is the load impedance. Given Zin = 75 ohms and ZL = 300 ohms, we can solve for Z0:
75 = (Z0^2) / 300
Z0^2 = 75 * 300
Z0 = sqrt(75 * 300)
Z0 = 150 ohms
Thus, the characteristic impedance (Z0) of the transmission line is 150 ohms.