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GATE ECE 2008 | Question-75

Common Data for Questions 74 and 75 :
The following series RLC circuit with zero initial conditions is excited by a unit impulse function $\delta(t)$.

 

 For $t>0$, the voltage across the resistor is

  1. $\frac{1}{\sqrt{3}}\left(e^{-\frac{\sqrt{3}}{2} t}-e^{-\frac{1}{2} t}\right)$
  2. $e^{-\frac{1}{2} t}\left[\cos \left(\frac{\sqrt{3} t}{2}\right)-\frac{1}{\sqrt{3}} \sin \left(\frac{\sqrt{3} t}{2}\right)\right]$
  3. $\frac{2}{\sqrt{3}} e^{-\frac{1}{2} t} \sin \left(\frac{\sqrt{3} t}{2}\right)$
  4. $\frac{2}{\sqrt{3}} e^{-\frac{1}{2} t} \cos \left(\frac{\sqrt{3} t}{2}\right)$
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