Practical Electronics/Parallel RC
Parallel RC[edit]
Circuit Impedance[edit]
Circuit Response[edit]
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle V = (IR  RC \frac {dV}{dt}) }
Parallel RL[edit]
Circuit Impedance[edit]
Circuit Response[edit]
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle I = I_R + I_L}
Parallel LC[edit]
Circuit Impedance[edit]
Circuit response[edit]
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle I = \frac{1}{L} \int V dt + C \frac{dV}{dt}}
Parallel RLC[edit]
Circuit Impedance[edit]
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle \frac{1}{Z} = \frac{1}{R} + \frac{1}{j\omega L} + j\omega C }
Circuit response[edit]
 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle I = I_R + I_L + I_C}
 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle I={\frac {V}{R}}+{\frac {1}{L}}\int Vdt+C{\frac {dV}{dt}}}
Natural Respond[edit]
Forced Respond[edit]
Second ordered equation that has two roots

 ω = α ±
Where

 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle \beta = \frac{1}{\sqrt{LC}}}
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle {\alpha^2 < \beta^2}} , 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle I = \frac{V}{2R}}
, 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  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle I = \frac {V}{R} + C\frac{dV}{dt}}  
Current  I  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle \frac {dV}{dt} = \frac{1}{C}(I  \frac{V}{R})}  
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 