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.

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.