Special Cases MCQ Quiz in मल्याळम - Objective Question with Answer for Special Cases - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

The source voltage ${\mathrm{V}}_{\mathrm{s}}$, source impedance ${\mathrm{R}}_{\mathrm{s}}$ and characteristic impedance ${\mathrm{R}}_{\mathrm{c}}$ can be modeled as

So, the voltage appearing across ${\mathrm{R}}_{\mathrm{c}}$ is ${\mathrm{V}}_{\mathrm{c}}=\frac{{\mathrm{R}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{s}}}$ . Now, as the voltage wave travels with a phase velocity $\mathrm{u}$, the wave takes a time $\mathrm{t}=\frac{{\mathrm{z}}_1}{\mathrm{u}}$ to reach point ${\mathrm{z}}_1$. Before $\mathrm{t}=\frac{{\mathrm{z}}_1}{\mathrm{u}}$, voltage at ${\mathrm{z}}_1$ remains zero and for $\mathrm{t}\ge \frac{{\mathrm{z}}_1}{\mathrm{u}};\mathrm{V}\left({\mathrm{z}}_1\right)=\frac{{\mathrm{R}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{s}}}$

Thus, we have the plot as

The initial current is decided by the characteristic impedance of the transmission line. This current wave once it reaches the load,a fraction of the curent is reflected back if the load is not matched. The reflected wave once it reaches back to the input end causes the net input current to be the sum of first forward wave and first reflected wave. This process continues and at $\mathrm{t}\to \mathrm{\infty }$, the current at the input(or at any point in general) is given by superposition of first forward, first reflected, second forward,$\dots \dots$, waves. ${\mathrm{I}}_{\mathrm{i}\mathrm{n}}={\mathrm{I}}_1^{+}+{\mathrm{I}}_1^{-}+{\mathrm{I}}_2^{+}+{\mathrm{I}}_2^{-}+\dots \dots$.

If the line is completely matched, then there is no reflected wave and the input current is constant for all times $\mathrm{t}\ge 0^{+}$.

Here, we know that the first forward input currect is $150\mathrm{m}\mathrm{A}$ is due to characteristic impedance. Let the characteristci impedance be ${\mathrm{Z}}_{\circ }$.\

Then, $\frac{{\mathrm{V}}_{\mathrm{i}\mathrm{n}}}{{\mathrm{Z}}_{\circ }}={\mathrm{I}}_{\mathrm{i}\mathrm{n}}(\mathrm{t}=0^{+})$

$\Rightarrow \frac{12}{{\mathrm{Z}}_{\circ }}=150\mathrm{m}\mathrm{A}\Rightarrow {\mathrm{Z}}_{\circ }=80\mathrm{\Omega }$

Notice that the new value of current at some time past $t=0$ is due to the superposition of first forward and first reflected wave. It can also be used to infer that the load is not matched to the line characteristic impedance as there is reflected wave.