Question

The input impedance of short circuited lossless line of length less than quarter wavelength is

• A. purely resistive
• B. purely capacitive
• C. purely inductive
• D. complex

Hint:

Shorted line < \(\lambda/4\) behaves like inductor.

Answer 1

The Correct Option is C

Concept: Input impedance of short-circuited line: \[ Z_{in} = jZ_0 \tan(\beta l) \]

Step 1: Nature of expression Contains imaginary unit \(j\).

Step 2: For small length \[ \beta l \lt \frac{\pi}{2} \]

Step 3: Behavior of tan function \(\tan(\beta l)\) is positive.

Step 4: Impedance nature \[ Z_{in} = +jX \Rightarrow \text{inductive} \]

Step 5: Conclusion \[ \boxed{\text{Purely inductive}} \]

Final Answer: \[ \boxed{(C)} \]