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Q&A Analysis of LC circuit using intuition

This problem investigates the behavior of the voltage across the capacitor in response to a step input: - I am asked to find the voltage Vc(t) without the use of differential equations or simula...

2 answers · posted 2mo ago by Carl‭ · last activity 2mo ago by Olin Lathrop‭

Question LC-network resonance circuit-analysis

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Carl‭ · 2024-09-10T12:39:47Z (2 months ago)

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This problem investigates the behavior of the voltage across the capacitor in response to a step input: -
![Image_alt_text](https://electrical.codidact.com/uploads/3098fcr6l3w1fyqp4hpupnygig2y)
I am asked to find the voltage Vc(t) without the use of differential equations or simulation. This is difficult but here is my attempt.
If the capacitor is much smaller than the inductors (say L1 = L2 = 1 mH and C1 = 1 pF) then C1's impedance is much higher than the inductors', and is effectively an open circuit. Hence, all the current through L1 equals the current through L2. If L1 and L2 have the same value then Vc becomes equal to 1/2 Vin.
If the components are of the same size (L1 = L2 = 1 mH and C1 = 1 mF) then it gets harder. Let's say 1 A passes through L1 and 0.8 A goes through L2 and 0.2 A goes through C1. Both L2 and C1 get energized but by currents of different magnitude and I suppose they seek to arrive at an equilibrium which would involve the voltage Vc having oscillations. I'm not sure about this explanation. Can someone help me out?

This problem investigates the behavior of the voltage across the capacitor in response to a step input: -
![Image_alt_text](https://electrical.codidact.com/uploads/3098fcr6l3w1fyqp4hpupnygig2y)
I am asked to find the voltage Vc(t) without the use of differential equations or simulation. This is difficult but here is my attempt.
If the capacitor is much smaller than the inductors (say L1 = L2 = 1 mH and C1 = 1 pF) then C1's impedance is much higher than the inductors', and is effectively an open circuit. Hence, all the current through L1 equals the current through L2. If L1 and L2 have the same value then Vc becomes equal to 1/2 Vin.
If the components are of the same size (L1 = L2 = 1 mH and C1 = 1 mF) then it gets harder. Let's say 1 A passes through L1 and 0.8 A goes through L2 and 0.2 A goes through C1. Both L2 and C1 get energized but by currents of different magnitude. I suppose L2 and C1 seek to arrive at some kind of energy equilibrium which would involve the voltage Vc having decaying oscillations. I'm not sure about this explanation. Can someone help me out?

#1: Initial revision by

Carl‭ · 2024-09-10T12:39:03Z (2 months ago)

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Analysis of LC circuit using intuition

This problem investigates the behavior of the voltage across the capacitor in response to a step input: -

![Image_alt_text](https://electrical.codidact.com/uploads/3098fcr6l3w1fyqp4hpupnygig2y)

I am asked to find the voltage Vc(t) without the use of differential equations or simulation. This is difficult but here is my attempt.

If the capacitor is much smaller than the inductors (say L1 = L2 = 1 mH and C1 = 1 pF) then C1's impedance is much higher than the inductors', and is effectively an open circuit. Hence, all the current through L1 equals the current through L2. If L1 and L2 have the same value then Vc becomes equal to 1/2 Vin.

If the components are of the same size (L1 = L2 = 1 mH and C1 = 1 mF) then it gets harder. Let's say 1 A passes through L1 and 0.8 A goes through L2 and 0.2 A goes through C1. Both L2 and C1 get energized but by currents of different magnitude and I suppose they seek to arrive at an equilibrium which would involve the voltage Vc having oscillations. I'm not sure about this explanation. Can someone help me out?

LC-network resonance circuit-analysis

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