Practical Electronics/Parallel RC
From Wikibooks, open books for an open world
Parallel RC[edit]
Circuit Impedance[edit]
Circuit Response[edit]
Parallel RL[edit]
Circuit Impedance[edit]
Circuit Response[edit]
Parallel LC[edit]
Circuit Impedance[edit]
Circuit response[edit]
Parallel RLC[edit]
Circuit Impedance[edit]
Circuit response[edit]
Natural Respond[edit]
Forced Respond[edit]
Second ordered equation that has two roots

 ω = α ±
Where
The current of the network is given by

 A e^{ω1 t} + B e^{ω2 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[edit]
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 ω_{1}  ω_{2} where ω_{1} = ω_{o}  Δω, ω_{2} = ω_{o} + 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
 ω_{1}  ω_{2} where
 ω_{1} = ω_{o}  Δω
 ω_{2} = ω_{o} + 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[edit]
Circuit  Symbol  Series  Parallel 

RC  
Impedance  Z  
Frequency  
Voltage  V  
Current  I  
Phase Angle  Tan θ = 1/2πf RC f = 1/2π Tan CR t = 2π Tan CR 
Tan θ = 1/2πf RC f = 1/2π Tan CR t = 2π Tan CR 