# voltage across the capacitor

Please answer #3 only.

You really don't have to derive the diff eq for the RLC circuit because we already know its of the form: s^2LC+sRC+1 =0, where v(t) = Ae^(st), dv/dt = sAe^(st) ...

** Please see the attached file for the full problem description **

In the above circuit, you may assume that i(0) = 0 and v(0) = 0

a) suppose L = 20 mH, C = 1 uF, R = 40 ohms, and is = 350 mA. Find v(t) for t >0.

b) suppose L = 0.25 H, C = 12.5 uF, R = 450 ohms, and is = 70 mA. Find v(t) for t >0.

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#### Solution Preview

** Please see the attached file for the complete solution response **

I still want to make it clear about how we get the above equations. Also, we need to take care of the current source.

All nodal voltages are labeled in the circuit.

In the s-domain, the capacitor is , the inductor is sL.

The current in the capacitor branch is: (please see the attached file)

Therefore, the voltage of nodal v1 is

(please see the attached file)

Then, the current in the resistor branch is

(please see the attached file)

Apply KCL for nodal v1, we have

(please see the attached file)

Rearrange the equation we have:

(*) (please see the attached file)

Pay attention to the right side of the ...

#### Solution Summary

This solution finds the voltage across the capacitor when t>0 in the RLC circuit. The solution is detailed and has a '5/5' rating.