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hi,
Just in case its homework I will give you a hint regarding the Requ ,,
Work out the value of the 25K and 6.25K resistors in parallel =...............................
Then work out the value of the 1K and the [parallel value] you have just calculated in series.
This will give you a ratio,,, now multiply the 30V by this ratio, what do you get.............
EDIT:
A quick look over the calculations show that the circuit diagram is wrong...
I read it as a semi-trick question... if the 30V source has been applied for a "long time" and the switch is opened a t=1mS, the question says, what is Vc at 4mS. Once the switch is opened, the capacitor is isolated from the source. That's a simple capacitor discharge question... what is the voltage across the cap after 3mS (4mS-1mS=3mS). The trick is what was the cap charged to before the switch was opened... and that's a resistor divider problem.
I read it as a semi-trick question... if the 30V source has been applied for a "long time" and the switch is opened a t=1mS, the question says, what is Vc at 4mS. Once the switch is opened, the capacitor is isolated from the source. That's a simple capacitor discharge question... what is the voltage across the cap after 3mS (4mS-1mS=3mS). The trick is what was the cap charged to before the switch was opened... and that's a resistor divider problem.
This appears to be a tricky question. The 'tricky' part comes in the way the voltage source is specified, in that it is NOT equal to 30u(t), but it is actually 30u(-t), and that minus t is the little tricky part
What this means is that we end up having to analyze three different circuit states (not just two):
1. With the voltage source of 30v that has been on for a 'long' time (implies a dc source of 30v)
2. With the voltage source when t is between 0 and 1ms (this is a little bit tricky)
3. With the voltage source when t is between 1ms and 4ms, especially at t=4ms.
Now #1 and #3 are quite apparent, in that we start off with 30v and sometime later the switch opens and we have a discharging RC circuit, which should be easy to calculate once we consider the in between step #2.
However, #2 is a little tricky because we have to go back to the definition of what u(t) really is, and if we look at that u(-t) for any positive value of t we end up with zero (0v).
So, #2 means that for the time period between t=0+ and t=1ms we have to consider the 'source' a short circuit. That means we have a second time constant to consider, which is obtained from the "Req" value. What else this means is that we end up with a different starting voltage for the last step's RC discharge, which is not equal to 25v any longer (but much lower) because of this second step.
Given the above information, i think you should be able to figure out the solution they are looking for. If not, just yell back here again, and if so, let us know the answer you got so we can compare notes...
Hint:
You should be able to get the same value they show as the solution without changing anything about the circuit.
I never said it was, what I said was... "Once the switch is opened, the capacitor is isolated from the source. That's a simple capacitor discharge question... " and, "The trick is what was the cap charged to before the switch was opened... and that's a resistor divider problem.", which would be true considering it was stated that the switch had been on for a "long time" ( I read that as infinitely long) which would mean that any time (t) varying transients were long gone.
I never said it was, what I said was... "Once the switch is opened, the capacitor is isolated from the source. That's a simple capacitor discharge question... " and, "The trick is what was the cap charged to before the switch was opened... and that's a resistor divider problem.", which would be true considering it was stated that the switch had been on for a "long time" ( I read that as infinitely long) which would mean that any time (t) varying transients were long gone.
I see that Al, picked up the point that 30V was switched off as a source, the source being of zero resistance, discharged the cap back thru the source, thru the Req, for 1mSec before the switch was opened.
Yes, at first we have 30v for a long time so the cap voltage has an initial voltage Vc(0).
Next, the cap discharges through three resistors in parallel for 1ms, which gives us a second cap voltage Vc(1ms).
Next, the switch opens and the cap discharges through one resistor for 3ms whcih gives us a third cap voltage Vc(4ms).
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