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RLC Series Current Graphing Calculator

\( \) \( \)\( \)\( \)

An online graphing calculator of the RLC series circuit current as a function the angular frequency \( \omega \) is presented.
This calculator graphs the amplitude \( | I | \) and phase \( P \) as a function of the angular frequecy \( \omega = 2 \pi f \) and calculates the frequency of resonnance \( \omega_r \), the lower and higher cutoff frequencies \( \omega_L \), \( \omega_H \), the quality factor \( Q \) and the bandwidth \( \Delta \omega \) of the RLC series circuit.

RLC Series Circuit

It has been shown that the current \( I \) in a series RLC circuit shown below.
series RLC circuit
is given by:
\[ I = \dfrac{V_0}{ \sqrt {R^2 + \left(\omega L - \dfrac{1}{\omega C} \right)^2} } \]
where \( V_0 \) is the peak value of the voltage source \( v_i = V_0 \cos (\omega t) \).
The frequency of resonance is defined as the frequency for which \( I \) is maximum and is given by.
\[ \omega_r = \dfrac{1}{\sqrt {L C}} \quad \quad (I) \]
This calculator calculate the amplitude \( |I| \) of the current \( I\) and its phase \( P \) defined as
\[ |I| = \sqrt {I_r^2 + I_i^2} \] \[ P = \arctan 2 (I_i , I_r) \] where \( I_r \) be the real part of \( I\) and let \( I_i \) be the imagianry part of \( I \).
The cutoff frequencies are:
\( \omega_L = \dfrac {- R C + \sqrt{ (R C)^2 + 4 L C }}{ 2 L C } \)

\( \omega_H = \dfrac {R C + \sqrt{ (R C)^2 + 4 L C}}{ 2 L C } \)
The bandwidth of the resonant circuit is defined by: \[ \Delta \omega = \omega_H - \omega_L \]
The quality factor \( Q \) is given by
\[ Q = \omega_r \dfrac{L}{R} \quad \quad \]
This calculator graphs the amplitude \( | I | \) and phase \( P \) as a function of the angular frequecy \( \omega = 2 \pi f \) and calculates \( \omega_r \), \( \omega_L \), \( \omega_H \), \( Q \) and \( \Delta \omega \) for \( V_0 = 1 \) Volt.


Current Versus Frequency Grapher

Step 1 : Enter the resistence R, the capaciatnce C and the inductance L.
(Ohms)
(Farads)
(Henry)

Step 2 : Enter the interval \( h \) beween points on the graph and adjust its value untill you get a graph that is easy to understand.
h =

Click on "Plot" ONCE ONLY and wait till the two graphs, amplitude and phase, are displayed.





More References and links

  1. Resonant Series RLC Circuit
  2. Resonant Series RLC Circuit Calculator
  3. RLC series circuits
  4. Series RLC Circuit Impedance Calculator
  5. Parallel RLC Circuit Impedance Calculator