In a loss less transmission line of length 50 cm with L = 10 μH/m, C = 40 pF/m is operated at 25 MHz. Its electrical path length is
$\frac{\pi}{2}$ radian
To find the electrical path length of a lossless transmission line, we use the given parameters: inductance per unit length \( L = 10 \, \mu \text{H/m} \) and capacitance per unit length \( C = 40 \, \text{pF/m} \), and operating frequency \( f = 25 \, \text{MHz} \).
The characteristic impedance \( Z_0 \) and the phase velocity \( v_p \) of the transmission line can be given by:
The phase velocity \( v_p \) is given by:
\(v_p = \frac{1}{\sqrt{LC}}\)
Substituting the given values:
\(v_p = \frac{1}{\sqrt{10 \times 10^{-6} \times 40 \times 10^{-12}}}\)
\(v_p = \frac{1}{\sqrt{400 \times 10^{-18}}}\)
\(v_p = \frac{1}{20 \times 10^{-9}}\)
\(v_p = 5 \times 10^{7} \text{m/s}.\)
The wavelength \( \lambda \) is given by:
\(\lambda = \frac{v_p}{f}\)
Substituting \( f = 25 \times 10^{6} \, \text{Hz} \), we have:
\(\lambda = \frac{5 \times 10^{7}}{25 \times 10^{6}} = 2 \, \text{m}\)
Now, the electrical path length of the line can be determined by how many wavelengths fit into the physical length of the line:
\(\text{Electrical path length} = \frac{\text{Physical Length}}{\lambda} \times 2\pi\)
In this case, the physical length = 50 cm = 0.5 m. So:
\(\text{Electrical path length} = \frac{0.5}{2} \times 2\pi\)
\(\text{Electrical path length} = \pi \, \text{radians}\)
Thus, the electrical path length in degrees is \( \frac{\pi}{2} \, \text{radian} \) (since \(\pi\) radians is equivalent to 180 degrees).
Therefore, the correct answer is: \(\frac{\pi}{2}\) radian.
Similar Questions
Consider the following statements
A. Reflection coefficient is change in the magnitude of reflected wave with constant phase with respect to incident wave.
B. Transmission coefficient is change in the magnitude and phase of transmitted wave with respect to incident wave
C. On smith chart, \(\dfrac{\lambda}{2}\) distance is equivalent to 2π.
D. For distortion less line, RL = GC
E. Directivity of an antenna can be less than 1 (unity).
Choose the most appropriate answer from the options given below :
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A lossless line has a characteristic impedance of 50 ohms. It is terminated in a load resistance of 75 ohms. The line is energised by a generator which has an output impedance of 50 ohms and an output voltage of 30 V (rms). The line is assumed to be 2.25 wavelength long. The input impedance and instantaneous load voltages are given :
(a) Zin = 50 ohms (b) VL (instantaneous) = 36 V (c) Zin = 33.33 ohms (d) VL (instantaneous) = 12 V
Which of the above are correct :
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(a) wave guide (b) Parallel wire (c) Rigid co-axial cables (d) Flexible co-axial cables
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(A) Support higher bandwidth than twisted pair cable
(B) Light weight
(C) Relatively expensive compared to twisted pair cable
(D) EMI resistant
(E) Doesn't at very high frequencyChoose the most appropriate answer from the options given below :
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Important Questions from Transmission Lines
A characteristic impedance does NOT satisfy which of the following statements?
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