# AC voltage source driving an inductor and a capacitor

## The Attempt at a Solution

I don't understand why would the current be zero in any of the branches . May be I am missing something very fundamental .

#### Attachments

• 33.9 KB Views: 530

Related Introductory Physics Homework Help News on Phys.org
cnh1995
Homework Helper
Gold Member
May be I am missing something very fundamental .
The question should be 'which ammeter may/could read zero ampere?'.
There is a specific value of ω for which one of the meters would read zero.

Jahnavi
The question should be 'which ammeter may/could read zero ampere?'.
There is a specific value of ω for which one of the meters would read zero.
OK .

cnh1995
Homework Helper
Gold Member
Have you studied electrical resonance?

Have you studied electrical resonance?
In series LCR circuit . But this is different .

cnh1995
Homework Helper
Gold Member
In series LCR circuit . But this is different .
What will happen at resonant frequency in this circuit? What is the effective impedance of this circuit at resonance?

Jahnavi
Sorry ! As I said I know only series LCR circuit .

cnh1995
Homework Helper
Gold Member
Sorry ! As I said I know only series LCR circuit .
Resonance occurs at a particular frequency where Xc=XL. In this circuit, what would be the equivalent reactance at resonance?

Jahnavi
In this circuit, what would be the equivalent reactance at resonance?
Equivalent reactance should be 0 . The net impedance should be equal to the resistance but since there is no resistance R in this circuit , net impedance Z will also be 0 .

cnh1995
Homework Helper
Gold Member
Equivalent reactance should be 0 . The net impedance should be equal to the resistance but since there is no resistance R in this circuit , net impedance Z will also be 0 .
No, the reactances are in parallel here.

Jahnavi
No, the reactances are in parallel here.
Should the equivalent reactance be infinite ?

cnh1995
Homework Helper
Gold Member
Should the equivalent reactance be infinite ?
Yes.

Yes.
OK . In that case current in A3 will be zero at resonance ?

cnh1995
Homework Helper
Gold Member
OK . In that case current in A3 will be zero at resonance ?
Yes.

Jahnavi
Yes.
OK .

Since the problem is done , could you explain what happens to the current in the other two branches at resonance .

cnh1995
Homework Helper
Gold Member
Here you can see that the source doesn't supply any current. This means the energy keeps oscillating between L and C and no power is drawn from the source.

Here you can see that the source doesn't supply any current. This means the energy keeps oscillating between L and C and no power is drawn from the source.
Is the frequency ω altered continuously till the circuit resonates at a particular frequency ?

I am asking this because some current has to flow through A3 initially so that energy could be stored in L/C .

cnh1995
Homework Helper
Gold Member
Is the frequency altered continuously till the circuit resonates at a particular frequency ?

I am asking this because some current has to flow through A3 initially so that energy could be stored in L/C .
Yes.
This is the sinusoidal steady-state scenario.
You don't have to know how the energy "gets into" the system. To analyse that, you need to do the transient analysis of the circuit using DEs and initial conditions, which is out of the scope of your curriculum (and this problem).

OK .

Perhaps one last question

What if the circuit is initially operated at the resonant frequency ? Would you say there will be no current in the circuit anytime anywhere ?

cnh1995
Homework Helper
Gold Member
Would you say there will be no current in the circuit anytime anywhere
That you need to see using transient analysis.
For the inductor,
Ldi/dt=Vmsin(ωt)
If you close the switch at t=0, you will get an undamped transient for the inductor current.
The transient depends on the instant of switching and magnitudes of R and L.
See
https://www.physicsforums.com/posts/5815132/
https://www.physicsforums.com/posts/5797346/

For the capacitor, there won't be any transient current for switching at t=0.

Overall you'll get the sum of these two currents as the resultant source current. I can't say much about its waveform or magnitude unless I do the math.

phoenix95
That means , in the transient period , there will be non zero current in A3 even at resonant frequency ?

cnh1995
Homework Helper
Gold Member
That means , in the transient period , there will be non zero current in A3 even at resonant frequency ?
Yes.
I'll try to find the exact equation for current once I reach home.

cnh1995
Homework Helper
Gold Member
Yes.
I'll try to find the exact equation for current once I reach home.
Here, after doing some math, you can see
iL(t)=Vm/ωL-Vmcos(ωt)/ωL

and
Ic(t)=Vmcos(ωt)/ωL
...(since ωL=1/ωC).
Therefore, the source current
Is(t)=IL+Ic
=Vm/ωL (or VmωC).

Thus, you can see if you connect the source at t=0 (i.e. at zero crossing of the input voltage), the current drawn from the source is dc.

Jahnavi
cnh1995
Homework Helper
Gold Member
Here is a simulation result of the same situation. It agrees with the math in #23.
For the values of L and C used, 159Hz is the resonant frequency.
You can see the source current(red) is dc.

#### Attachments

• 27 KB Views: 150
• 36.1 KB Views: 135
Last edited:
Thanks !