Chemical Engineering
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Match the items in Column $A$ with the items in Column $B$

$\begin{array}{|cl|cI|}\hline
&\text{$Column\:A$} & \text{$Column\:A$}  \\ \hline &\text{P. Pure dead-time} & \text{I. $\phi =-90^{\circ}$}  \\  &\text{Q. Pure capacitive} & \text{II. $\frac{K_{1}}{s}-\frac{K_{2}}{\tau s+1}$ with $K_{2}> \tau K_{1}$} \\ &\text{R. Inverse response} & \text{III. $0<AR<1$} \\ 
&\text{S. First-order process with unit gain} & \text{IV. $AR=1$} \\ \hline \end{array}$

Here, $\phi$ denotes the phase shift, $K_{1}$ and $K_{2}$ the process gains, $\tau$ the time constant, and $AR$ the amplitude ratio.

  1. $P-II,\:Q-III,\:R-IV,\:S-I$
  2. $P-III,\:Q-II,\:R-IV\:S-I$
  3. $P-I,\:Q-IV,\:R-II,\:S-III$
  4. $P-IV,\:Q-I,\:R-II,\:S-III$
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