Exams › GATE › Technical

An extra-high-voltage transmission line of length 300 km can be approximated by a lossless line having propagation constant $\beta = 0.00127$ radians per km. Then the percentage ratio of line length to wavelength will be

1. 24.24 %
2. 12.12 %
3. 19.05 %
4. 6.06 %

Correct answer: 6.06 %

Solution

For a lossless line, the phase constant is related to wavelength by $\beta = 2\pi/\lambda$. Using $\beta = 0.00127$ rad/km gives $\lambda \approx 4948$ km. The ratio $300/4948 \times 100$ is about 6.06%, so the correct answer is 6.06%.

Related GATE Technical questions

• One end of a lossless transmission line having characteristic impedance 75 \(\Omega\) and length 1 cm is short-circuited. At 3 GHz, the input impedance at the other end of the transmission line is
• For a parallel-plate transmission line, let $v$ be the speed of propagation and $Z$ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of 2 results in
• A 3-phase transmission line is shown in the figure. The voltage drop across the transmission line is given by the following equation: $\begin{bmatrix}\Delta V_a\\ \Delta V_b\\ \Delta V_c\end{bmatrix}=\begin{bmatrix}Z_s&Z_m&Z_m\\ Z_m&Z_s&Z_m\\ Z_m&Z_m&Z_s\end{bmatrix}\begin{bmatrix}I_a\\ I_b\\ I_c\end{bmatrix}$. Shunt capacitance of the line can be neglected. If the line has positive-sequence impedance of $15\,\Omega$ and zero-sequence impedance of $48\,\Omega$, then the values of $Z_s$ and $Z_m$ will be
• In a long transmission line, if $r$, $l$, $g$, and $c$ are the resistance, inductance, shunt conductance, and capacitance per unit length, respectively, the condition for distortionless transmission is
• A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given \(\mu_0=4\pi\times10^{-7}\,\text{H/m}\) and \(\varepsilon_0=\dfrac{10^{-9}}{36\pi}\,\text{F/m}\), the characteristic impedance of the cable is
• The three-dimensional state of stress at a point is given by $\sigma = \begin{bmatrix}10 & 0 & 0\\0 & 40 & 0\\0 & 0 & 0\end{bmatrix}$ MPa. The maximum shear stress at the point is

⚔️ Practice GATE Technical free + battle 1v1 →