Final answer:
Deriving vo/vs involves applying Ohm's law and Kirchhoff's laws to relate output voltage across a component to the source voltage and considering impedance if the circuit has reactive components.
Step-by-step explanation:
To derive an expression for vo/vs in a circuit, we generally need to analyze the circuit components and apply the relevant laws such as Ohm's law and the laws of series and parallel circuits. The specifics of the circuit in question (referenced as Figure p1.19 in the original question) are not provided, so a general approach would involve identifying resistors, capacitors, inductors, and their arrangement. Then, using Ohm's law (V = IR) and Kirchhoff's voltage and current laws, one could set up equations that relate the output voltage across a specific component (vo) to the source voltage (vs).
If the circuit contains reactive components like capacitors and inductors, their reactance must be considered. Capacitive reactance (Xc) and inductive reactance (XL) can be calculated using their formulas, Xc = 1/(ωC) and XL = ωL, where ω is the angular frequency of the AC source. Subsequently, these values are used to find the total impedance of the circuit, from which the current can be derived. The voltage across each element is then V = IZ, where Z represents the impedance of the element.
Lastly, the power dissipated by each circuit element can also provide insight into the voltage relations, where for resistors, P = I2R = V2/R. For the source, the power can be alternately defined as P = IV. By equating the power across the components and the source, one can isolate and solve for the desired voltage ratio vo/vs.