GATE IN 2017 Question Paper (12-Feb-2017) (Shift 2)

A series R-L-C circuit is excited with a 50 V, 50 Hz sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor (V${}_L$) is _____ V.

The connection of two 2-port networks is shown in the figure. The ABCD parameters of N₁ and N₂ networks are given as

{≤ft[ {*20c A&B\\ C&D } ]_N_1} = ≤ft[ {*20c 1&5\\ 0&1 } ]and {≤ft[ {*20c A&B\\ C&D } ]_N_2} = ≤ft[ {*20c 1&0\\ 0.2&1 } ]



The ABCD parameters of the combined 2-port network are

A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at Node 1 is - 1 V, then the voltage at Node 2 is ________ V.

A periodic signal x(t) is shown in the figure. The fundamental frequency of the signal x(t) in Hz is __________.

A system is described by the following differential equation:

$\frac{dy\left(t\right)}{dt}+2y\left(t\right)=\frac{dx\left(t\right)}{dt}+x\left(t\right),x\left(0\right)=y\left(0\right)=0$

Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is