I'm currently brushing up on RLC circuits for an upcoming final exam, but I haven't encountered one as difficult as this kind of circuit. It asks to solve for RC, the voltage V2 across the R2 resistor, and the the total energy delivered to the capacitor.
Despite knowing that the time constant (for RC circuits) is RC, I'm uncertain as to whether I ended up with the right equivalent resistance, Req, that's used to find the time constant. I was under the assumption that by using the condition for t > 0 (or @ infinity) to find Req, I knew that the cap is in series with the resistor R1, suggesting that Req > 3k ohms... Upon further calculation, the Req came out to be 5000 ohms, leading to a time constant of 25 ms. I'm not certain if this was done right however.
For the voltage across resistor: by presuming that at for t<0 and t=0, the cap has 0 V, meaning that R1 should be parallel to R2, leading to Vr2(0) (the voltage across R2) = 1.5k/7.5k = 0.2V. After several time constants, I thought that the cap is fully charged at t = inf. Here is where I'm really confused: do I ignore R1 at this point, since the cap acts as a open circuit? I felt that this would make Vr2(t=0+) a potential divider problem. As such, since there is no current flowing in it (if dV/dT~=0), this would lead to get R2  R3 = 3k, hence t=T0+ leads to 1V * 3k/(3k+ 6k) = 1/3V as the steady state condition! From there, I believed that between the 2 steady states, we have an exponential rise given by the time constant of the circuit. Can anyone verify whether I took a correct method to finding the voltage across resistor R2?
Finally, the real deal is solving for the total energy delivered to capacitor. My knowledge tells me that for the initial voltage of the cap, it is 0 V, since it is assumed as a fully discharged capacitor. However, I have no idea what is the condition for it at t = 0+. I suspect that that while the capacitor would usually reach steady state at t = inf, the voltage of capacitor is not 1 V. Beyond that, I have no idea how to actually solve for the energy delivered at this condition. Does anyone have ideas, suggestions, or advice as to how to do this?
Despite knowing that the time constant (for RC circuits) is RC, I'm uncertain as to whether I ended up with the right equivalent resistance, Req, that's used to find the time constant. I was under the assumption that by using the condition for t > 0 (or @ infinity) to find Req, I knew that the cap is in series with the resistor R1, suggesting that Req > 3k ohms... Upon further calculation, the Req came out to be 5000 ohms, leading to a time constant of 25 ms. I'm not certain if this was done right however.
For the voltage across resistor: by presuming that at for t<0 and t=0, the cap has 0 V, meaning that R1 should be parallel to R2, leading to Vr2(0) (the voltage across R2) = 1.5k/7.5k = 0.2V. After several time constants, I thought that the cap is fully charged at t = inf. Here is where I'm really confused: do I ignore R1 at this point, since the cap acts as a open circuit? I felt that this would make Vr2(t=0+) a potential divider problem. As such, since there is no current flowing in it (if dV/dT~=0), this would lead to get R2  R3 = 3k, hence t=T0+ leads to 1V * 3k/(3k+ 6k) = 1/3V as the steady state condition! From there, I believed that between the 2 steady states, we have an exponential rise given by the time constant of the circuit. Can anyone verify whether I took a correct method to finding the voltage across resistor R2?
Finally, the real deal is solving for the total energy delivered to capacitor. My knowledge tells me that for the initial voltage of the cap, it is 0 V, since it is assumed as a fully discharged capacitor. However, I have no idea what is the condition for it at t = 0+. I suspect that that while the capacitor would usually reach steady state at t = inf, the voltage of capacitor is not 1 V. Beyond that, I have no idea how to actually solve for the energy delivered at this condition. Does anyone have ideas, suggestions, or advice as to how to do this?
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