Consider the following block diagram in the figure.

The transfer function $\frac{C (s)}{R (s)}$ is

\frac{G_{1} G_{2}}{1 + G_{1} G_{2}}

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G_{1} G_{2} + G_{1} + 1

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G_{1} G_{2} + G_{2} + 1

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\frac{G_{1}}{1 + G_{1} G_{2}}

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Solution

The correct option is C $G_{1} G_{2} + G_{2} + 1$

Converting the block diagram into signal fow graph on

Forward paths,
$P_{1} = G_{1} G_{2}; P_{2} = G_{2} .1; P_{3} = 1.1 = 1$
So, the transfer function is
$\frac{C (s)}{R (s)} = G_{1} G_{2} + G_{2} + 1$

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