Hi people, i need to know what steps i should go through to solve the problem i have, please help me with some hints or maybe you know where i could find solved similar problem, it will help me a lot to understand this chapter.

the task: before the instant of time t=0, the key is open, the circuit is in the steady state and no energy is stored in the capacitor. At t=0s the key is switched to the"1" position and then, at t=2s it is switched to the "2" position. Find and draw the waveform uc(t) for -1s<=t<=10s.
given R=1kΩ, E=2V, C=2mF.



Thanks a lot guys!

 

When the switch is turned on pos. 1, the capacitor will start to charge itself from the voltage source. The time constant of that circuit is RC, and at t=2s, the capacitor will have acquired a certain voltage.

When the switch is turned on pos. 2, the source is left out of the circuit and the capacitor will be left free to discharge through the two resistors, with a time constant of 2RC.

Does that help you?

 

It's an example of a capacitor charge / discharge sequence.

When the switch connects to position "1" the capacitor begins to charge from the source E via a series resistor R. So in the interval from 0 to 2 seconds the capacitor voltage will rise from 0V to a value you should be able to determine. Call the voltage at time t=2 seconds uc(2).

When the switch is then transfered to position "2" the capacitor will begin to discharge from the aforementioned value uc(2) through a total series resistance of 2R. Eventually the capacitor will fully discharge. So from 2 to 10 seconds the voltage will reduce from uc(2) to a lower value uc(10) - again you should be able to determine the value uc(10), based on your understanding of simple capacitor discharge.