Derive a power balance equation for the RL and RC circuits. (See Problem 5.) Discuss the significance of the signs of the three power terms.
The power balance equation for RL and RC circuit are and respectively.
The governing differential equation for RC circuit is .
The power dissipated by a circuit is and the power dissipated by an inductor is and the power associated by a capacitor is .
So, the equation is
Therefore, the power balance equation for RL circuit is .
Further, solve the above expression
Therefore, the power balance equation for RC circuit is
Early Monday morning, the temperature in the lecture hall has fallen to , the same as the temperature outside. At , the janitor turns on the furnace with the thermostat set at . The time constant for the building is and that for the building along with its heating system is . Assuming that the outside temperature remains constant, what will be the temperature inside the lecture hall at ? When will the temperature inside the hall reach ?
It was noon on a cold December day in Tampa: 16°C. Detective Taylor arrived at the crime scene to find the sergeant leaning over the body. The sergeant said there were several suspects. If they knew the exact time of death, then they could narrow the list. Detective Taylor took out a thermometer and measured the temperature of the body: 34.5°C. He then left for lunch. Upon returning at 1:00 p.m., he found the body temperature to be 33.7°C. When did the murder occur? [Hint: Normal body temperature is 37°C.]
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