Parallel Resonance Circuit Assignment Help

Electrostatics - Parallel Resonance Circuit

Physics Assignment Help >> Electrostatics >> Parallel Resonance Circuit

A parallel resonance circuit consists of a coil of inductance L and a condenser of capacity C joined in parallel to a source of alternating as shown in fig 1

Let the alternating supplied by the source be 

E = E0 sin w t 

As current through L lags behind the applied alternating by a phase angle π/2, therefore, we may write the value of current through L at a particular instant of time t as 
I L = E0/XL sin (w t – π/2)

Again as current through C leads the applied alternating by a phase angle π/2 therefore we may write the value of current through C at same instant t as 

I c = E0/XC sin (ω T + π/2) 

The total current I in the circuit at this instant is, therefore, I = IL + IC

I = E0/XL sin (wt – π/2) + E0/XC sin (w t + π/2)

I = E0/XL (- cos wt) + E0/Xc cos wt = E0 cos w t [- 1/XL + 1/XC]

I = E0 cos wt [ - 1/wL + wc]

When w [(C – 1)/wL] = 0

W C = 1/w L or w2 = 1/LC

Or w = 1 /√LC or 2 π v = 1/√LC

V = 1/2π √LC

Frequency of applied alternating emf becomes equal to natural frequency of oscillation of the circuit. Thence resonance occurs. The circuit is called parallel resonance circuit and this frequency v is called parallel resonance frequency. Under this conduction eq. shows that I = 0 at parallel resonance frequency, the resonance circuit does not allow any current to flow through it, as shown in  fig 2 the impedance of parallel resonance circuit at this frequency must obviously be maximum.

The parallel resonance circuits are used in the transmitting circuit. They reject the currents corresponding to parallel resonance frequencies, and allow other frequencies to pass through. Such circuits are therefore called filter circuits or rejecter circuits or even anti resonance circuits. 

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