RLC 8-1-2020

An RLC circuit is excited by a DC voltage source. At time t = 0 t = 0 , the inductors and capacitors are de-energized. Let P M O P_{M O} be the maximum instantaneous power that ever flows out of the source, and let P M I P_{MI} be the maximum instantaneous power that ever flows into the source.

What is P M O P M I \large{\frac{P_{M O}}{P_{M I}}} ? Give your answer as a positive number.

Details and Assumptions:
1) V S = 10 V_S = 10
2) R 1 = R 2 = L 1 = L 2 = C 1 = C 2 = C 3 = 1 R_1 = R_2 = L_1 = L_2 = C_1 = C_2 = C_3 = 1


The answer is 8.68.

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1 solution

Karan Chatrath
Aug 2, 2020

I S I_S is the source current and I B I_B is the current through the element-less branch of the 'wheat-stone bridge'. Circuit equations:

I S = I C 2 + I L 2 I_S = I_{C2} + I_{L2} I C 3 = I R 2 + I L 2 I_{C3} = I_{R2} + I_{L2} I C 2 = I R 2 + I B I_{C2} = I_{R2} + I_{B}

I S = Q ˙ S I_S = \dot{Q}_{S} I C 2 = Q ˙ 2 I_{C2} = \dot{Q}_{2} I C 3 = Q ˙ 3 I_{C3} = \dot{Q}_{3}

V S + R 1 I S + Q S C 1 + L 1 I ˙ S + Q 2 C 2 = 0 -V_S + R_1I_S + \frac{Q_S}{C_1} +L_1\dot{I}_S + \frac{Q_2}{C_2}=0 L 2 I ˙ L 2 = Q 2 C 2 + R 2 I R 2 L_2\dot{I}_{L2} = \frac{Q_2}{C_2} + R_2I_{R2} R 2 I R 2 + Q 3 C 3 = 0 R_2I_{R2} + \frac{Q_3}{C_3}=0

Numerical integration does the rest. Leaving out those details.

The instantaneous power supplied by the source is:

@Karan Chatrath please check last 2 hour notifications.

Talulah Riley - 10 months, 2 weeks ago

@Karan Chatrath share your python code .
Thanks in advance.

Talulah Riley - 10 months, 2 weeks ago

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Please show your attempt.

Karan Chatrath - 10 months, 2 weeks ago

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@Karan Chatrath did you edited it
It was written perhaps??

Talulah Riley - 10 months, 2 weeks ago

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@Talulah Riley No, I did not edit it. I did not share the code in my solution.

Karan Chatrath - 10 months, 1 week ago

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