Consider the second-order RC circuit shown in Figure 6.77. Assume that all the initial conditions are zero.

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Consider the second-order RC circuit shown in Figure 6.77. Assume that all the initial conditions are zero.

a. Use the node or loop method to derive the input-output differential equation relating \(v_{\mathrm{o}}\) and \(v_{\mathrm{a}}\), and find the transfer function \(V_{\mathrm{o}}(s) / V_{\mathrm{a}}(\mathrm{s})\).

b. Use the impedance method to determine the transfer function \(V_{\mathrm{o}}(s) / V_{\mathrm{a}}(\mathrm{s})\), and compare with the result obtained Part (a).

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