Resonansi a Zabe RLC
Amsa RLC circuit da na resistor, inductor da capacitor suna cikin voltage supply. Wannan series RLC circuit yana da alaka mai kyau da take resonating a kan tushen da ake kira resonant frequency.
A wannan circuit da ke da inductor da capacitor, energy ta fito a biyu abubuwa daban-daban.
Idan current ta fadada a inductor, energy ta fito a magnetic field.
Idan capacitor ta shaida, energy ta fito a static electric field.
Magnetic field a inductor ta fara ne a kan current, wanda ake bayar da discharging capacitor. Saboda haka, capacitor ta shaida a kan current da ake bayar da collapsing magnetic field of inductor kuma wannan yanayi ta ci gaba, tana haɗa electrical energy zuwa magnetic field da electric field. A wasu lokutan, a kan tushen da ake kira resonant frequency, inductive reactance ta zama da capacitive reactance wanda ya haɗa electrical energy zuwa electric field of the capacitor da magnetic field of the inductor. Wannan ta fara harmonic oscillator for current. A RLC circuit, presence of resistor tana haɗa waɗannan oscillation to die out over period of time and is called damping effect of resistor.
Variation in Inductive Reactance and Capacitive Reactance with Frequency
Variation of Inductive Reactance Vs Frequency
Na sani inductive reactance XL = 2πfL means inductive reactance is directly proportional to frequency (XL and prop ƒ). Idan frequency ya fi zero ko a kasu DC, inductive reactance ya fi zero, circuit ta yi aiki a matsayin short circuit; amma idan frequency ya ɗaya; inductive reactance ya ɗaya. A infinite frequency, inductive reactance ta zama infinity and circuit behaves as open circuit. Yana nufin cewa, idan frequency ya ɗaya inductive reactance ya ɗaya and idan frequency ya rage, inductive reactance ya rage. Don haka, idan mutum ya kula graph between inductive reactance and frequency, it is a straight line linear curve passing through origin as shown in the figure above.
Variation of Capacitive Reactance Vs Frequency
It is clear from the formula of capacitive reactance XC = 1 / 2πfC that, frequency and capacitive reactance are inversely proportional to each other. In case of DC or when frequency is zero, capacitive reactance becomes infinity and circuit behaves as open circuit and when frequency increases and becomes infinite, capacitive reactance decreases and becomes zero at infinite frequency, at that point the circuit acts as short circuit, so the capacitive reactance increases with decease in frequency and if we plot a graph between capacitive reactance and frequency, it is an hyperbolic curve as shown in figure above.
Inductive Reactance and Capacitive Reactance Vs Frequency
From the above discussion, it can be concluded that the inductive reactance is directly proportional to frequency and capacitive reactance is inversely proportional to frequency, i.e at low frequency XL is low and XC is high but there must be a frequency, where the value of inductive reactance becomes equal to capacitive reactance. Now if we plot a single graph of inductive reactance vs frequency and capacitive reactance vs frequency, then there must occur a point where these two graphs cut each other. At that point of intersection, the inductive and capacitive reactance becomes equal and the frequency at which these two reactances become equal, is called resonant frequency, fr.
At resonant frequency, XL = XL
At resonance f = fr and on solving above equation we get,
Variation of Impedance Vs Frequency
At resonance in series RLC circuit, two reactances become equal and cancel each other. So in resonant series RLC circuit, the opposition to the flow of current is due to resistance only. At resonance, the total impedance of series RLC circuit is equal to resistance i.e Z = R, impedance has only real part but no imaginary part and this impedance at resonant frequency is called dynamic impedance and this dynamic impedance is always less than impedance of series RLC circuit. Before series resonance i.e before frequency, fr capacitive reactance dominates and after resonance, inductive reactance dominates and at resonance the circuit acts purely as resistive circuit causing a large amount of current to circulate through the circuit.
Resonant Current
In series RLC circuit, the total voltage is the phasor sum of voltage across resistor, inductor and capacitor. At resonance in series RLC circuit, both inductive and capacitive reactance cancel each other and we know that in series circuit, the current flowing through all the elements is same, So the voltage across inductor and capacitor is equal in magnitude and opposite in direction and thereby they cancel each other. So, in a series resonant circuit, voltage across resistor is equal to supply voltage i.e V = Vr.
In series RLC circuit current, I = V / Z but at resonance current I = V / R, therefore the current at resonant frequency is maximum as at resonance in impedance of circuit is resistance only and is minimum.
The above graph shows the plot between circuit current and frequency. At starting, when the frequency increases, the impedance Zc decreases and hence the circuit current increases. After some time frequency becomes equal to resonant frequency, at that point inductive reactance becomes equal to capacitive reactance and the impedance of circuit reduces and is equal to circuit
