Consider the RLC circuit of Figure. Parts of this problem are repeated from Problem. Use t...

Consider the RLC circuit of Figure. Parts of this problem are repeated from Problem. Use those results if available.

(a) Write the state equations of the circuit, with the state variables equal to the current i(t) and the capacitor voltage υC(t), and the output equal to the υC(t).

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(b) Use the results of Part (a) to find the circuit transfer function.

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(c) Use the s-plane impedance approach to verify the transfer function of Part (b). Recall that for the impedance approach, the impedance of the inductance is sL and of the capacitance is 1/(sC).

Consider the RLC circuit of Figure. The circuit input voltage is υi(t).

(a) Write the state equations for the circuit, with the state variables equal to the current i(t), the capacitor voltage υC(t), and the output equal to υC(t).

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(b) Write the state equations of the circuit, with the state variables equal to i(t) and υC(t), and the output equal to i(t).