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# Resonance in an LR circuit?

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#### jonnybgood

##### Full Member level 4
Why am I asked to find the frequancy at which an LR circuit is resonant? Every formula that I saw always included a negative reactance for a capacitor in series.

the circuit to be resonant must be RLC
if you have a circuit consists of
Ac supply
and inductor of 1 Henry
capacitor 1F (not practical but take for example)

and resistor of 1 ohm
connected all of them in series
then this circuit has two elements that frequency dependent
and they are the capacitor and indcutor
why?

inductor impedence = +J2(pi)LF
j for imaginary number
2pi is constant
L inductor henry
F frequency
so from this equation we found that it is a function of F and L
and it makes an angle
the larger the impedence of the inductor the larger the angled and more lag is the current

capacitor

capacitor impedence = 1/(j2pi * F C)
j for imaginary number
2pi is constant
C capacitance
F frequency
so from this equation we found that it is a function of F and C
and it makes an angle
the larger the impedence of the inductor the larger the angled and more lag is the VOLTAGE

so we have two parameters
XL = 2pi FL
XC=-1/(2Pi FC) multiple the above and below by J so we have negative sign

back to the circuit
we have
the total impedence
z= R+j xl-jXC
z= R +j(Xl-XC)

||z||= sqrt (R^2+(XL-Xc)^2) as a magnitude
and we have angle theta = tan( (xl-xc) / R)

the frequency at which XL=XC
then we have impedence of resistive load at this frequency and the circuit is call to be at resonant
at this frquency
for series circuit the impedence is minimum
iin contrast to parallel RLC circuit at which the impedence is maximum

jonnybgood

### jonnybgood

Points: 2
Yeah it refreshed all I have been studying last month.. i assume " inductor" and "inductance" in the capacitor paragraph had to be capacitor and capacitance.

thanks again

Brandon

MahmoudHassan

Points: 2