## Series and Parallel Resonance Assignment Help

Assignment Help: >> AC Circuits - Series and Parallel Resonance

Series and Parallel Resonance:

Resonance is that condition in any AC circuit at a specific frequency, while the applied voltage and resultant current are in same phase. Thus, at resonance the power factor of the AC circuit is unity and it acts like a pure resistive circuit.

Series Resonance

In series RLC circuit at a specific frequency when inductive reactance (XL = ωL) becomes equal to the capacitive reactance ( X C =   1/ ωC  ), then the circuit is said to be at resonance

XL = XC

In the series RLC circuit of Figure, the circuit current I is specified by Figure: Series Resonance Circuit

I =( V/ Z)  A

where Z represents the equivalent impedance of the circuit.

Z = R + j ωL +(1/ j ωC)

= R + j ωL -(1/ ωC)j

Z = R + j ( X L  - X C )

where

X L        = ωL and  XC    =   1/ ωC

= R +  jX

where (XL - XC) = X (Net Reactance)

Therefore

I =        V / (R + j ( X L - X C ))  = V / R +  jX    Amp Figure: Voltage and Current Phasor

And voltage drop across resistance, R is VR = IR (in phase with I)

Voltage drop across inductance, L is VL = I XL (leading I by 90o)

Voltage drop across capacitance, C is VC = I XC (leading I by 90o)

The phasor diagram of the variables of the entire circuit is shown in Figure Figure: Voltage Vector Diagram of RLC Series Circuit

 Admittance Curve Band Width Impedance Curve Parallel Resonance Voltage Vector Diagram #### Assured A++ Grade

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