For the system shown in figure below, what is the transfer function $\frac{V_{o} (s)}{V_{i} (s)}$ ?

\frac{V_{o} (s)}{V_{i} (s)} = \frac{s L}{s^{2} R L C + s L + R}

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\frac{V_{o} (s)}{V_{i} (s)} = \frac{s L R}{s^{2} R L C + s L R + R}

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\frac{V_{o} (s)}{V_{i} (s)} = \frac{s^{2} L}{s^{2} R L C + 2 s L + 1}

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\frac{V_{o} (s)}{V_{i} (s)} = \frac{s}{s^{2} R L C + s L + R}

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Solution

The correct option is A $\frac{V_{o} (s)}{V_{i} (s)} = \frac{s L}{s^{2} R L C + s L + R}$
Applying Laplace transform and taking the parallel combination of L and C gives $\frac{\frac{L s}{C s}}{L s + \frac{1}{C s}}$

Applying voltage division rule we get, $V_{o} (s) = \frac{\frac{L / C}{L s + \frac{1}{C s}}}{R + \frac{L / C}{L s + \frac{1}{C s}}} V_{i} (s)$

$\frac{V_{o} (s)}{V_{i} (s)} = \frac{s L}{s^{2} R L C + s L + R}$

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