Practice Problem 7.12 Fundamentals Of Electric Circuits Patched -

IL(s) = Vi(s) / (R1 + L1s)

iL(t) + C1(dv0(t)/dt) + v0(t)/R2 = 0

Applying KCL at the node where the inductor, capacitor, and resistor R2 are connected, we get: practice problem 7.12 fundamentals of electric circuits

To find the transfer function H(s) = V0(s)/Vi(s), we need to analyze the circuit using Laplace transform techniques. The transfer function is a mathematical representation of the relationship between the input and output voltages of a circuit.

where iL(t) is the current through the inductor. IL(s) = Vi(s) / (R1 + L1s) iL(t)

IL(s) + C1sV0(s) + V0(s)/R2 = 0

Assuming zero initial conditions (i.e., v0(0) = 0 and iL(0) = 0), we can simplify the equations: and resistor R2 are connected

Simplifying further:

Taking the Laplace transform of the KCL and KVL equations, we get: