In the circuit below, the switch reaches a steady state while in position 1 then at t = 0 gets thrown to position 2. I am supposed to find the voltage (s-domain) across the capacitor under these conditions using thev. theorem(adsbygoogle = window.adsbygoogle || []).push({});

I just want to make sure I am approaching the problem with the correct methods:

1. Find initial conditions using the properties that an inductor is shorted in steady state and a capacitor is open circuit

I got i(0) = 5 A

v(0) = 5 V

2. Transform the circuit to the s-domain, adding an independent voltage source with voltage = 10 (from inductor). Remove the capacitor to make it an open circuit. Find V_{TH}via voltage divider equation.

3. Find Z_{eq}by shutting off all independent sources.

Z_{eq}= 2 + (1 || (1 + 2s))

4. Recreate the circuit with V_{TH}and Z_{eq}in a loop with the 1/2 F capacitor and 5/s V independent voltage source from the initial conditions (steady state).

5. KCL to get current

6. voltage across the cap = current * capacitor value in s domain

mainly i want to know if my initial conditions are correct and if i'm using them correctly.

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# 2-position switch circuit

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