If the voltage waveform depicted below is applied across the terminals of a 2 mF capacitor, determine the expressions and plot the following: (a) The resulting current, i(t). (b) The resulting power, p(t). (c) The resulting energy, w(t). Clearly indicate the value on the y-axis for the limits of each time interval. Is energy being stored or delivered by the capacitor? What is the value of the maximum energy stored in the capacitor?

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 the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct.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.