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Munnu

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- Homework Statement
- What is the initial energy store in the capacitor?

How long does it take for the capacitor to discharge to 50% of the initial stored energy?

In the following circuit, how long will it take the initial energy stored in the capacitor to increase to 50% of the final value?

- Relevant Equations
- u=0.5CV^2

V_c=V_0*e^(t/RC)

V_c=V_source*(1-e^(-t/RC))

This is not my homework. I took it upon myself to answer a textbook question for mental stimulation. I wanted to know if someone can verify if these were the correct values that needed to be solved for, process, and final answer, and if not, what needed to be considered.

For the initial voltage stored in the capacitor, I got 20V. I used thevenin’s theorem to get R_th=60 ohm, V_th=20V; V_c is V_th. Then I used capacitor discharge equation V_c=V_0*e^(t/RC) where t=0. V_c=20V*e^0=20V.

For the initial voltage stored in the capacitor, I got 20V. I used thevenin’s theorem to get R_th=60 ohm, V_th=20V; V_c is V_th. Then I used capacitor discharge equation V_c=V_0*e^(t/RC) where t=0. V_c=20V*e^0=20V.

**What is the initial energy store in the capacitor?**- Is it 0.1 watt-second (joule), are we looking for the joules unit of measurement? I calculated using u=0.5CV^2, where C=0.5mF and V_c=20V (calculated , thevenin)

**How long does it take for the capacitor to discharge to 50% of the initial stored energy?**- Do I divide u=0.1 joule in half? What I did was u=0.5CV^2 where u=0.1joule/2. I solved for voltage using that formula. The voltage at the halfway stored energy is 14.14V. After solving for the voltage V_c=14.14V and a prior calculation of our V_0=20V (via thevenin’s), I used V_c=V_0*e^(-t/RC); RC=0.03s. I got t=0.010s.

**In the following circuit, how long will it take the initial energy stored in the capacitor to increase to 50% of the final value?**- u=0.5CV^2 where u=0.1/2 joule, where the voltage at the halfway stored energy is 14.14V I used V_c=V_source*(1-e^(-t/RC)); RC=0.03s, V_source=20V. I got t=0.0368s.
- Note: V_c in this scenario is where the voltage would be when energy stored u=0.1/2 (50% energy stored) , V_source is the initial voltage stored in the capacitor.