GATE EC 2017 Question Paper (05-Feb-2017) (Shift 2)

The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0.



The current i(t) (in ampere) at t = 0.5 seconds is __________

Consider the circuit shown in the figure.



The Thevenin equivalent resistance (in Ω) across P-Q is ___________

Consider an LTI system with magnitude response

≤ft| H≤ft( f ) | = ≤ft\{ {*20c {1 - ≤ft| f |20,}&≤ft| f | ≤ 20\\ 0,&≤ft| f | > 20 } .

and phase response arg {H(f)} = -2f.

If the input to the system is

$x\left(t\right)=8\cos \left(20\pi t+\frac{\pi }{4}\right)+16\sin \left(40\pi t+\frac{\pi }{8}\right)+24\cos \left(80\pi t+\frac{\pi }{16}\right).$

Then the average power of the output signal y(t) is ____________.

The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = [sin (t)/πt] u(t), where u(t) is a unit step function, the system output y(t) as t → ∞ is ________.

Consider the parallel combination of two LTI systems shown in the figure.



The impulse response of the systems are

h₁(t) = 2δ(t + 2) - 3δ(t + 1)

h₂(t) = δ(t - 2).

If the input x(t) is a unit step signal, then the energy of y(t) is ___________ .