Consider the RLC circuit shown in Figure 6.78. Assume zero initial conditions.

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

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

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FIGURE 6.78 Problem 4. RC RL ww