Final answer:
The magnitude of the voltage on the short-circuited transmission line can be sketched as a standing wave pattern. It exhibits maxima and minima along the transmission line. At points where the voltage is at its maximum, there is constructive interference, and at points of minimum voltage, there is destructive interference.
Step-by-step explanation:
The student is asking for a sketch of the magnitude of the voltage and current on a short-circuited transmission line exhibiting a standing wave pattern. The given voltage function is V(z) = V₀ e⁻ᵉβz + V₀ e⁺ᵉβz, where V₀ is the maximum voltage amplitude, and β is the phase constant related to the wavelength λ. From this equation, we can infer that the standing wave will have nodes and antinodes along the line. The nodes are where the voltage is zero, and antinodes are where the voltage is at its maximum value.
Given the transmission line is short-circuited, there will be nodes at the short-circuited end because the voltage must be zero at that point. The antinodes, where the voltage is maximum, will be a half wavelength (λ/2) away from the nodes. Current nodes and voltage antinodes will occur at the same points because the current is zero where the voltage is at its peak due to the short-circuited boundary condition.
Conversely, voltage nodes and current antinodes will also align, meaning maximum current will occur where the voltage is zero. The pattern will repeat every half wavelength along the line. Sketching the voltage and current would show an alternating pattern of nodes and antinodes, with the distance between consecutive nodes or antinodes being λ/2.