E.2 Use the voltage divider rule to find the transfer function Vo(s)/Vi(s) of the circuit in Fig. E.3(a). Show that the transfer function can be made independent of frequency if the condition C1R1 = C2R2 applies. Under this condition the circuit is called a compensated attenuator. Find the transmission of the compensated attenuator in terms of R1 and R2.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.