CR DC circuit

[bill papas]

Hi guys im in my first year of university studying mechanical engineering.
I have a course on basic electronics and we have been assigned a problem of a CR circuit connected to a dc power source.
I have spent over 10 hours trying to solve this problem but have still not made any headway. is there a chance someone could walk me through how to solve it or reference me to a solution with the same circuit?
thank you for any help provided in advance

 

[Laplace]

These type of problems are so simple they are solved by inspection. The procedure was covered in a recent post:

But you should not try to over-think the solution. My linear circuits textbook had a section on how to analyze switched (aka step response) RC & RL circuits with one energy storage element, and how to do it graphically because there are only two possibilities (and duality applies, i.e., capacitor current behaves the same as inductor voltage, and capacitor voltage behaves the same as inductor current.)

So the two possibilities are as follows for quantity 'X' when switched at t=0:
1: 'X' starts with an initial value, then decays to zero.
2: 'X' slowly rises from zero to its final value.
If #1, use X=(initial value)∙e^(-t/τ)
If #2, use X=(final value)∙(1-e^(-t/τ))
where τ is the time constant, either R∙C or L/R

Note that the initial slope of the exponential curve is such that 'X' would achieve its final value in one time constant. Also note that some circuits may have constant offsets involved but this discussion only applies to the transient behavior. You could generalize the equations for non-zero offsets. Thevenin equivalent of the resistor portion of the circuit may be necessary.

So for any switched RC or RL circuit where the 'X' is the capacitor or inductor voltage or current, you just need to decide whether the waveform rises or decays from t=0 and decide what the initial or the final value is.

One just needs to realize that in this circuit at t=0 the capacitor is a 'short-circuit' and at t=infinity the capacitor is an 'open circuit', so figure the initial and final values with that in mind.

Note that the last time I used a differential equation to solve a circuit problem was back in the 1960's so I don't have a clue how to do it now.

 

[Ratch]

Hi guys im in my first year of university studying mechanical engineering.
I have a course on basic electronics and we have been assigned a problem of a CR circuit connected to a dc power source.
I have spent over 10 hours trying to solve this problem but have still not made any headway. is there a chance someone could walk me through how to solve it or reference me to a solution with the same circuit?
thank you for any help provided in advance


View attachment 19158

View attachment 19159

Find the current as shown in the attachment. Then multiply by R to get the voltage. Easiest to find the current by Laplace transforms, but the classical solution is shown in the image below.

Ratch