Practical Electronics/Parallel RC

Parallel RC 200px|A parallel RC Circuit Circuit Impedance Circuit Response Parallel RL 200px|An RL parallel circuit\ Circuit Impedance Circuit Response Parallel LC 100px|LC circuit diagram Circuit Impedance Circuit response Parallel RLC 200px Circuit Impedance Circuit response Natural Respond Forced Respond Second ordered equation that has two roots ω = -α ± Where The current of the network is given by A eω1 t + B eω2 t From above When , there is only one real root ω = -α When , there are two real roots ω = -α ± When , there are two complex roots ω = -α ± j Resonance Response At resonance, the impedance of the frequency dependent components cancel out . Therefore the net voltage of the circui is zero and At Resonance Frequency . . Current is at its maximum value Further analyse the circuit At ω = 0, Capacitor Opened circuit . Therefore, I = 0 . At ω = 00, Inductor Opened circuit . Therefore, I = 0 . With the values of Current at three ω = 0 , , 00 we have the plot of I versus ω . From the plot If current is reduced to halved of the value of peak current , this current value is stable over a Frequency Band ω1 - ω2 where ω1 = ωo - Δω, ω2 = ωo + Δω In RLC series, it is possible to have a band of frequencies where current is stable, ie. current does not change with frequency . For a wide band of frequencies respond, current must be reduced from it's peak value . The more current is reduced, the wider the bandwidth . Therefore, this network can be used as Tuned Selected Band Pass Filter . If tune either L or C to the resonance frequency . Current is at its maximum value . Then, adjust the value of R to have a value less than the peak current by increasing R to have a desired frequency band . If R is increased from R to 2R then the current now is which is stable over a band of frequency ω1 - ω2 where ω1 = ωo - Δω ω2 = ωo + Δω For value of I < . The circuit respond to Wide Band of frequencies . For value of < I > . The circuit respond to Narrow Band of frequencies Summary Circuit Symbol Series Parallel RCthumbnail|100pxright|framed|A parallel RC CircuitImpedanceZ Frequency VoltageV CurrentI Phase Angle Tan θ = 1/2πf RC f = 1/2π Tan CR t = 2π Tan CRTan θ = 1/2πf RC f = 1/2π Tan CR t = 2π Tan CR