The figure shows reactance as the function of line length Fig. (a): a short circuited transmission lineFig. (b): an open- circuited transmission lineThe vertical lines are repeated for equal intervals of λ/4.Which of the following is valid :(i) For Short Circuit Line: Input impedance along line length between 0 to λ/4 is Inductive(ii) For Open Circuit Line: Input impedance along line length between 0 to λ/4 is Capacitive
Question
The figure shows reactance as the function of line length Fig. (a): a short circuited transmission lineFig. (b): an open- circuited transmission lineThe vertical lines are repeated for equal intervals of λ/4.Which of the following is valid :(i) For Short Circuit Line: Input impedance along line length between 0 to λ/4 is Inductive(ii) For Open Circuit Line: Input impedance along line length between 0 to λ/4 is Capacitive
Solution 1
(i) For Short Circuit Line: Input impedance along line length between 0 to λ/4 is Inductive
To determine the validity of this statement, we need to analyze the figure provided. In Fig. (a), which represents a short-circuited transmission line, we observe vertical lines that are repeated at equal intervals of λ/4.
According to the figure, the reactance as a function of line length is shown. Specifically, we are interested in the input impedance along the line length between 0 to λ/4.
If we examine the graph, we can see that the reactance increases as we move from 0 to λ/4. This indicates that the input impedance is inductive during this range. Therefore, the statement (i) is valid for a short circuit line.
(ii) For Open Circuit Line: Input impedance along line length between 0 to λ/4 is Capacitive
Similarly, we need to analyze the figure to determine the validity of this statement. In Fig. (b), which represents an open-circuited transmission line, we again observe vertical lines repeated at equal intervals of λ/4.
By examining the reactance graph, we can see that the reactance decreases as we move from 0 to λ/4. This indicates that the input impedance is capacitive during this range. Therefore, the statement (ii) is valid for an open circuit line.
In summary, for a short circuit line, the input impedance is inductive along the line length between 0 to λ/4, while for an open circuit line, the input impedance is capacitive along the line length between 0 to λ/4.
Solution 2
(i) For Short Circuit Line: Input impedance along line length between 0 to λ/4 is Inductive
To determine the validity of this statement, we need to analyze the figure provided. In Fig. (a), which represents a short-circuited transmission line, we can observe vertical lines that are repeated at equal intervals of λ/4.
According to the figure, the reactance as a function of line length is shown. From 0 to λ/4, the reactance increases, indicating that the input impedance is inductive. Therefore, the statement (i) is valid for a short circuit line.
(ii) For Open Circuit Line: Input impedance along line length between 0 to λ/4 is Capacitive
Similarly, we need to analyze the figure to determine the validity of this statement. In Fig. (b), which represents an open-circuited transmission line, we can again observe the vertical lines repeated at equal intervals of λ/4.
From the figure, we can see that the reactance decreases from 0 to λ/4, indicating that the input impedance is capacitive. Therefore, the statement (ii) is valid for an open circuit line.
In summary, for a short circuit line, the input impedance is inductive along the line length between 0 to λ/4, while for an open circuit line, the input impedance is capacitive along the line length between 0 to λ/4.
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