# Equations during resonance

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#### Archit

##### Member
I have attached the following circuit in which resonance is happening. Initial voltage of capacitor C1 is Vo , ie Vc1(0)=Vo. Vc2(0)=0. there is zero initial current through inductor Lk. Please provide mathematical equations derived from basic KVL and KCL equations happening here during resonance.
I need to show that after quarter period of resonance one of the C1 will discharge completely and C2 will charge to Vo.
Thanking in anticipation.
EDIT1 Assume C1=C2= Cp

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#### Tony Stewart

##### Well-Known Member
Parallel tank cct needs a current source. Never a voltage source then V ratio is never 0 an Vmax rather it is C1/C2

#### Ratchit

##### Well-Known Member
I have attached the following circuit in which resonance is happening. Initial voltage of capacitor C1 is Vo , ie Vc1(0)=Vo. Vc2(0)=0. there is zero initial current through inductor Lk. Please provide mathematical equations derived from basic KVL and KCL equations happening here during resonance.
I need to show that after quarter period of resonance one of the C1 will discharge completely and C2 will charge to Vo.
Thanking in anticipation.
A quarter period starting for where? At t=0, or when the circuit reaches steady state?. If at t=0, you need to do a transient analysis, so you need to set up the differential equation. What is the period of Vo? How are you going to achieve resonance, by changing the L C values, or the frequency of Vo?

Ratch

#### Archit

##### Member
A quarter period starting for where? At t=0, or when the circuit reaches steady state?. If at t=0, you need to do a transient analysis, so you need to set up the differential equation. What is the period of Vo? How are you going to achieve resonance, by changing the L C values, or the frequency of Vo?

Ratch
Vo is a dc voltage source. L and C values are fixed. t=0 meaning the time when the circuit conditions are given ie when vc1=vo and il=0

#### Ratchit

##### Well-Known Member
I have attached the following circuit in which resonance is happening. Initial voltage of capacitor C1 is Vo , ie Vc1(0)=Vo. Vc2(0)=0. there is zero initial current through inductor Lk. Please provide mathematical equations derived from basic KVL and KCL equations happening here during resonance.
I need to show that after quarter period of resonance one of the C1 will discharge completely and C2 will charge to Vo.
Thanking in anticipation.
EDIT1 Assume C1=C2= Cp
OK, I think I have the equations you are look for. Do you want to publish your solution before I disclose mine?

Ratch

#### Ratchit

##### Well-Known Member
Parallel tank cct needs a current source. Never a voltage source then V ratio is never 0 an Vmax rather it is C1/C2
Question: How can a current source at the resonant frequency send current through a parallel tank circuit when its impedance is infinity? Isn't that like a unstoppable force trying to push an immovable object?

Ratch

#### Archit

##### Member
OK, I think I have the equations you are look for. Do you want to publish your solution before I disclose mine?

Ratch
Vc1=Vo*coswt
Vc2=Vo*(1-coswt)

#### Archit

##### Member
Question: How can a current source at the resonant frequency send current through a parallel tank circuit when its impedance is infinity? Isn't that like a unstoppable force trying to push an immovable object?

Ratch
are you getting same?

Vc1=Vo*coswt
Vc2=Vo*(1-coswt)