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For the block diagram as shown in figure, the overall transfer function \(\frac{C}{R}\) is

For the block diagram as shown in figure, the overall transfer function \(\frac{C}{R}\) is Correct Answer <span class="math-tex">\(\frac{{{G_1}{G_2}}}{{\left( {1 + {G_1}{H_1} - {G_2}{H_2}} \right)}}\)</span>

Concept:

Some standard block diagram reduction rules are shown below:

[ alt="F2 U.B Madhu 30.12.19 D10" src="//storage.googleapis.com/tb-img/production/20/05/F2_U.B_Madhu_30.12.19_D10.png" style="width: 349px; height: 106px;">

[ alt="F2 U.B Madhu 30.12.19 D11" src="//storage.googleapis.com/tb-img/production/20/05/F2_U.B_Madhu_30.12.19_D11.png" style="width: 342px; height: 106px;">

Application:

Given block diagram is shown below:

[ alt="F2 U.B Madhu 30.12.19 D12" src="//storage.googleapis.com/tb-img/production/20/05/F2_U.B_Madhu_30.12.19_D12.png" style="width: 371px; height: 151px;">

We have to shift this take-off point at forward G2 block.

[ alt="F2 U.B Madhu 30.12.19 D13" src="//storage.googleapis.com/tb-img/production/20/05/F2_U.B_Madhu_30.12.19_D13.png" style="width: 389px; height: 169px;">

[ alt="F2 U.B Madhu 30.12.19 D14" src="//storage.googleapis.com/tb-img/production/20/05/F2_U.B_Madhu_30.12.19_D14.png" style="width: 361px; height: 124px;">

[ alt="F2 U.B Madhu 30.12.19 D15" src="//storage.googleapis.com/tb-img/production/20/05/F2_U.B_Madhu_30.12.19_D15.png" style="width: 293px; height: 81px;">

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