1
GATE ECE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A lossless microstrip transmission line consists of a trace of width w. It is drawn over a practically infinite ground plane and is separated by a dielectric slab of thickness 𝑡 and relative permittivity $${\varepsilon _r}\, > \,1$$. The inductance per unit length and the characteristic impedance of this line are L and $$Z_o$$ respectively. GATE ECE 2016 Set 2 Electromagnetics - Transmission Lines Question 1 English Which one of the following inequalities is always satisfied?
A
$${Z_o}\, > \,\sqrt {{{Lt} \over {{\varepsilon _o}\,{\varepsilon _r}\,w}}} $$
B
$${Z_o}\, < \,\sqrt {{{Lt} \over {{\varepsilon _o}\,{\varepsilon _r}\,w}}} $$
C
$${Z_o}\, > \,\sqrt {{{Lw} \over {{\varepsilon _o}\,{\varepsilon _r}\,t}}} $$
D
$${Z_o}\, < \,\sqrt {{{Lw} \over {{\varepsilon _o}\,{\varepsilon _r}\,t}}} $$
2
GATE ECE 2016 Set 2
Numerical
+1
-0
Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $$ > 0 is a constant. When the vector magnitude $$\left| I \right|$$ is at its minimum value, the angle $$\theta $$ that I makes with the x axis (in degree, such that $$0\, \le \,0 \le \,180$$) is _________________
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3
GATE ECE 2016 Set 2
Numerical
+1
-0
Light from free space is incident at an angle $${\theta _1}$$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $${n_1}\,\, = \,\,1.5$$ and $${n_2}\,\, = \,\,1.4$$ respectively. GATE ECE 2016 Set 2 Electromagnetics - Miscellaneous Question 5 English

The maximum value of $${\theta _1}$$ (in degrees) for which the incident light will be guided in the core of the fibre is ________ .

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4
GATE ECE 2016 Set 2
Numerical
+2
-0
Consider a region of silicon devoid of electrons and holes, with an ionized donor density of $${\mathrm N}_\mathrm d^+=10^{17}\;\mathrm{cm}^{-3}$$. The electric field at x = 0 is 0 V/cm and the electric field at x = L is 50 kV/cm in the positive x direction. Assume that the electric field is zero in the y and z directions at all points. GATE ECE 2016 Set 2 Electronic Devices and VLSI - PN Junction Question 4 English

Given q = 1.6 × 10−19 coulomb, $$\varepsilon$$0 = 8.85 × 10−14 F/cm, $$\varepsilon$$r = 11.7 for silicon, the value of L in nm is ________.

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