In a series RLC circuit, the output is taken across the capacitor
A. <span class="math-tex">\(\frac{s}{{\left( {1 + sRC + {s^2}LC} \right)}}\)</span>
B. <span class="math-tex">\(\frac{{sC}}{{\left( {1 + sRC + {s^2}LC} \right)}}\)</span>
C. 1 + sRC + s<sup>2</sup>LC
D. <span class="math-tex">\(\frac{1}{{\left( {1 + sRC + {s^2}LC} \right)}}\)</span>
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Right Answer is: D
SOLUTION
A series RLC circuit with the input applied at the resistor and ground and output taken across the capacitor is drawn as:
Replacing C with 1/sC, and L with sL, the equivalent circuit is redrawn as:
Applying voltage division rule, the voltage across the capacitor is calculated as:
\(V_c(s)=V_i(s)\times \frac{\frac{1}{sC}}{\frac{1}{sC}+sL+R}\)
The closed-loop transfer function will be:
\(\frac{V_c(s)}{V_i(s)}=\frac{\frac{1}{sC}}{\frac{1}{sC}+sL+R}\)
\(\frac{V_c(s)}{V_i(s)}=\frac{1}{{\left( {1 + sRC + {s^2}LC} \right)}}\)
