Question

The open-circuit and short-circuit impedances measured at the input terminals of a lossless transmission line are -j500 and 50 respectively. The characteristic impedance of the line is a) ja (b) 2512 (c) S002 (a -J1000​

Answer 1

Correct Question:

The open-circuit and short-circuit impedances measured at the input terminals of a lossless transmission line are -j500 and 50 respectively. The characteristic impedance of the line is

a) 158.11 (b) 2512 (c) S002 (a -J1000​

Final Answer:

The characteristic impedance of the lossless transmission line, whose open-circuit and short-circuit impedances measured at the input terminals of a  are -j500 and 50 respectively, is 158.11.

Hence, the correct option is option a.

Given:

The open-circuit and short-circuit impedances measured at the input terminals of a lossless transmission line are -j500 and 50 respectively.

To Find:

The characteristic impedance of the line and the correct option

Explanation:

The characteristic impedance of the lossless transmission line is equal to the square root of the sum of the open-circuit and short-circuit impedances measured at its input terminals.

Step 1 of 2

The open-circuit impedance of the lossless transmission line is

$={Z_{OC}\\=-j500$

The short-circuit impedance of the lossless transmission line is

$={Z_{SC}\\=50$

Step 2 of 2

The characteristic impedance is

$=\sqrt{Z_{OC} *Z_{SC}} \\=\sqrt{500 *50} \\\\=\sqrt{25000} \\=158.11$

The characteristic impedance of the lossless transmission line, whose open-circuit and short-circuit impedances measured at the input terminals of a  are -j500 and 50 respectively, is 158.11.

Hence, the correct option is option a.

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Answer 2

The characteristic impedance of the line is 158.11

• The ratio of the voltage and current amplitudes of a single wave propagating through a uniform transmission line—i.e., a wave travelling in one direction without encountering reflections in the opposite direction—is known as the characteristic impedance or surge impedance (often written $Z_{0}$). It can also be described as the input impedance of a transmission line with an infinite length, which is equivalent. Characteristic impedance, for a uniform line, is independent of length and is defined by the geometry and materials of the transmission line. The ohm is the characteristic impedance's SI unit.
• A lossless transmission line's characteristic impedance is entirely genuine and devoid of any reactive elements. Such a wire does not lose energy in the process of transmitting energy from a source at one end to the other. The source perceives a transmission line of limited length (lossless or lossy), terminated at one end with an impedance matching the characteristic impedance, as being infinitely long and there are no reflections.

Here, according to the given information, we are given that,

The open-circuit and short-circuit impedances measured at the input terminals of a lossless transmission line are -j500 and 50 respectively.

Then, the open circuit impedance is -j500 and that of short circuit is 50.

Then, the characteristic impedance of the line is,

$\sqrt{500.50} \\=158.11$

Hence, the characteristic impedance of the line is 158.11

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