The RLC Circuit:
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bphgravity
Senior Member
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Re: The RLC Circuit:
Z = sqrt R? + X?
Z = sqrt R? + X?
Ed MacLaren
Senior Member
Re: The RLC Circuit:
Ed
[ February 04, 2005, 08:33 PM: Message edited by: Ed MacLaren ]
The power factor is unity at the resonant frequency. At that frequency the inductive and capacitive reactances cancel.
Ed
[ February 04, 2005, 08:33 PM: Message edited by: Ed MacLaren ]
Ed MacLaren
Senior Member
Re: The RLC Circuit:
Ed
Wouldn't you have to give us some circuit component values in order for us to calculate the resonant frequency?
Ed
Re: The RLC Circuit:
Ed,
I am looking for the general formula for resonant frequency which you have provided. No need to plug in numbers.
I still have not seen the general formula for impedance in terms of R, L, C, w, and the operator, "j".
I feel that understanding the general formula is of prime importance. Certainly in a quiz or homework, you would want some values.
Ed,
I am looking for the general formula for resonant frequency which you have provided. No need to plug in numbers.
I still have not seen the general formula for impedance in terms of R, L, C, w, and the operator, "j".
I feel that understanding the general formula is of prime importance. Certainly in a quiz or homework, you would want some values.
crossman
Senior Member
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- Southeast Texas
Re: The RLC Circuit:
the "operator j" ??
my ignorance is showing on that one
As for Z = Sqrt(R^2 + X^2), that is only for a series LCR circuit.
Z of parallel is the reciprocal of the sqrt of the (reciprocal of R) squared + the (reciprocal of X) squared, something like that.
But in parallel, I prefer to calculate the RMS branch currents, then add them up vectorially using the "current triangle" giving us the RMS total current. Then divide the RMS source voltage by the RMS total current and there ya have Z for the parallel circuit.
For the resonant frequency, Inductive reactance = capacitive reactance. Setting these two items equal in an equation, then a little algebra, will arrive at the formula that Ed posted.
Clue me in about this "operator j"
the "operator j" ??
my ignorance is showing on that one
As for Z = Sqrt(R^2 + X^2), that is only for a series LCR circuit.
Z of parallel is the reciprocal of the sqrt of the (reciprocal of R) squared + the (reciprocal of X) squared, something like that.
But in parallel, I prefer to calculate the RMS branch currents, then add them up vectorially using the "current triangle" giving us the RMS total current. Then divide the RMS source voltage by the RMS total current and there ya have Z for the parallel circuit.
For the resonant frequency, Inductive reactance = capacitive reactance. Setting these two items equal in an equation, then a little algebra, will arrive at the formula that Ed posted.
Clue me in about this "operator j"
Ed MacLaren
Senior Member
Re: The RLC Circuit:
Compare-
Ed
[ February 05, 2005, 07:58 AM: Message edited by: Ed MacLaren ]
It's a way of denoting, in an equation, that a number is a vector quantity.
Compare-
Ed
[ February 05, 2005, 07:58 AM: Message edited by: Ed MacLaren ]
Ed MacLaren
Senior Member
Re: The RLC Circuit:
Ed
As long as we're all having fun anyway, what is the impedance of this parallel circuit.
Ed
Re: The RLC Circuit:
Ed, I just knew you were doing to do that. I won't spoil your party though.
Another way to look at parallel circuits is to use admittance which is the inverse of impedance, conductance which is the inverse of resistance, and susceptance which the inverse of reactance. The units are Siemens--used to be Mhos which makes more sense.
Maybe someone can convert this problem to admittance, conductance, and susceptance?
Ed, I just knew you were doing to do that. I won't spoil your party though.
Another way to look at parallel circuits is to use admittance which is the inverse of impedance, conductance which is the inverse of resistance, and susceptance which the inverse of reactance. The units are Siemens--used to be Mhos which makes more sense.
Maybe someone can convert this problem to admittance, conductance, and susceptance?
crossman
Senior Member
- Location
- Southeast Texas
Re: The RLC Circuit:
the circuit is close to being a "tank" circuit and I will assume that was your intention.
Inductive reactance = 20 ohms
capacitive reactance = 20 ohms
RMS current in inductive branch = 6 amps
RMS current in capacitive branch = 6 amps
total current is the vector sum of these two currents... they are 180 dergrees out of phase
so total current = zero
and impedance = infinity (or very darned close to it )
If you put an ammeter between the capacitor and the inductor, it will read 6 amps even though the total current is 0 amps.
This is a cool circuit to hook up on our Lab Volt equipment... there is a little bit of resistive current that will show up on the total current ammeter, but not much.... very instructive
the circuit is close to being a "tank" circuit and I will assume that was your intention.
Inductive reactance = 20 ohms
capacitive reactance = 20 ohms
RMS current in inductive branch = 6 amps
RMS current in capacitive branch = 6 amps
total current is the vector sum of these two currents... they are 180 dergrees out of phase
so total current = zero
and impedance = infinity (or very darned close to it
)If you put an ammeter between the capacitor and the inductor, it will read 6 amps even though the total current is 0 amps.
This is a cool circuit to hook up on our Lab Volt equipment... there is a little bit of resistive current that will show up on the total current ammeter, but not much.... very instructive
Re: The RLC Circuit:
Sam, my AC Circuits text was by Kerchner & Corcoran. Another from that era was by Tang.
Now, I have been hinting that someone should say that the impedance of the RLC series circuit is given by,
Z = R +j(wL - 1/wC)
By inspection we see that a high frequency yields an inductive impedance, while a low frequency yields a capacitive impedance. Between those extremes lies the resonant frequency at which
Z = R + j0 and PF = 1.
Sam, my AC Circuits text was by Kerchner & Corcoran. Another from that era was by Tang.
Now, I have been hinting that someone should say that the impedance of the RLC series circuit is given by,
Z = R +j(wL - 1/wC)
By inspection we see that a high frequency yields an inductive impedance, while a low frequency yields a capacitive impedance. Between those extremes lies the resonant frequency at which
Z = R + j0 and PF = 1.
Re: The RLC Circuit:
Now if we add a 20 Ohm resistor to Ed's parallel circuit, we would have 6A of real current and 720W. This is the scenario I postulated in my 3-phase teaser. Take away the L and C, and we still have 720W. The parallel reactive elements have no effect on power. KW, not KVA.
Now if we add a 20 Ohm resistor to Ed's parallel circuit, we would have 6A of real current and 720W. This is the scenario I postulated in my 3-phase teaser. Take away the L and C, and we still have 720W. The parallel reactive elements have no effect on power. KW, not KVA.
Re: The RLC Circuit:
Ed's parallel circuit demonstrates in prinicple the use of capacitors to correct power factor. Take away the cap, and you are left with a lagging current.
Now if we assume a 20 Ohm real load, same inductance, and no cap, what is the total current with phase angle please? Remember, this is a parallel circuit.
Ed's parallel circuit demonstrates in prinicple the use of capacitors to correct power factor. Take away the cap, and you are left with a lagging current.
Now if we assume a 20 Ohm real load, same inductance, and no cap, what is the total current with phase angle please? Remember, this is a parallel circuit.
crossman
Senior Member
- Location
- Southeast Texas
Re: The RLC Circuit:
6 amps in the inductive branch
6 amps in the resistive branch
total current is the hypotenuse of a right triangle with the two 6's as sides = 8.49 amps
phase angle is 45 degrees which can be found by using trig with the triangle
oh.... phase angle is lagging
impedance =120/8.49 = 14.13 ohms
power factor = cos45 = .707 or 70.7%
all the above is RMS
don't try any of this with instantaneous values.
[ February 07, 2005, 12:40 PM: Message edited by: crossman ]
6 amps in the inductive branch
6 amps in the resistive branch
total current is the hypotenuse of a right triangle with the two 6's as sides = 8.49 amps
phase angle is 45 degrees which can be found by using trig with the triangle
oh.... phase angle is lagging
impedance =120/8.49 = 14.13 ohms
power factor = cos45 = .707 or 70.7%
all the above is RMS
don't try any of this with instantaneous values.
[ February 07, 2005, 12:40 PM: Message edited by: crossman ]
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