Final answer:
To derive the expression for vo/vs, one must apply Ohm's law and understand series and parallel circuits' equivalent resistances. Calculate total resistance for combined circuits, find total current, and then compute the output voltage in terms of the source voltage.
Step-by-step explanation:
To derive an expression for vo/vs for the given circuit, it's important to understand Ohm's law and the concept of equivalent resistance. For series and parallel circuits, resistances add differently. In a series circuit, the total resistance is the sum of individual resistances (Rtot = R1 + R2 + ...), while in a parallel circuit, the inverse total resistance is the sum of the inverses of individual resistances (1/Rp = 1/R1 + 1/R2 + ...).
Using Ohm's law (V = IR), where V is the voltage, I is the current, and R is the resistance, we can find the total current in the circuit as I = V/Rtot. Once the total current is known, the voltage across any component in series with the source can be found by multiplying the current by the resistance of that component (V1 = IR1). Similarly, the voltage across resistors in parallel is the same, and total current is divided among them according to their resistances.
In the case of combined series and parallel circuits, the equivalent resistances need to be calculated for the separate parts of the circuit before these can be combined to find the total resistance. The final step is to use the calculated total current and resistance values to derive the output voltage (vo) in relation to the source voltage (vs).