LRC Circuit - Why able to drop cos from equation

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KindofSlow

Junior Member
Joined
Mar 5, 2010
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Hello All,

Working on a physicsproblem regarding an LRC circuit, and more specifically what isthe time required for the charge amplitude to drop to half its starting value?

I correctly started withthis equation.

½ Q = Q0e(-Rt/2L)cos(w’t+ɸ)

I got stuck trying tofigure out what to do with the cosine part of equation. So I checked the answerand it shows I can just drop it, and solve this:

e(-Rt/2L) = ½

I can easily solve thisequation for t.



I'm pretty sure ɸ is zero so I can’tfigure out why cos(w’t) cancels or gets eliminated or can be dropped?


As always, any and allinsights greatly appreciated.

Thank you



 
KindofSlow said:
Hello All,

Working on a physics problem regarding an LRC circuit, and more specifically what is the time required for the charge amplitude to drop to half its starting value?

I correctly started with this equation.

½ Q = Q0e(-Rt/2L)cos(w’t+ɸ)

I got stuck trying tofigure out what to do with the cosine part of equation. So I checked the answerand it shows I can just drop it, and solve this:

e(-Rt/2L) = ½

I can easily solve this equation for t.

I'm pretty sure ɸ is zero so I can’t figure out why cos(w’t) cancels or gets eliminated or can be dropped?

As always, any and allinsights greatly appreciated.

Thank you
Click to expand...

What is the definition of amplitude?
 
Amplitude is max height. In this case, max Q, and also starting Q.
Since this occurs at t=0, and cos(0) = 1, I thought maybe this term became 1 so dropped for that reason.
But this seems wrong since we're solving for t, not setting t=0.
So I'm obviously missing something.
I'll keep thinking.
Thank you
 
KindofSlow said:
Hello All,

Working on a physicsproblem regarding an LRC circuit, and more specifically what isthe time required for the charge amplitude to drop to half its starting value?

I correctly started withthis equation.

½ Q = Q0e(-Rt/2L)cos(w’t+ɸ)

I got stuck trying tofigure out what to do with the cosine part of equation. So I checked the answerand it shows I can just drop it, and solve this:

e(-Rt/2L) = ½

I can easily solve thisequation for t.



I'm pretty sure ɸ is zero so I can’tfigure out why cos(w’t) cancels or gets eliminated or can be dropped?


As always, any and allinsights greatly appreciated.

Thank you
Click to expand...
To say it a different way than Subhotosh Khan did: The amplitude factor is Q0e(-Rt/2L) and the phase factor is the cosine term.
 
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