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Formula Maximum current in resonant RLC series circuit Peak voltage    Ohmic resistance    Inductance    Capacitance    Angular frequency

Formula
Formula: Maximum current in resonant RLC series circuit

Peak current

Unit
This is the maximum current (also called peak current) flowing through a RLC series circuit. Of course, the current \( I(t) \) oscillates periodically with time, but \( I_0 \) indicates the peak value.

The formula is similar to Ohm's law, except that instead of Ohm's resistance \(R\) we have the magnitude of the impedance \( | Z | \):$$ | Z | ~=~ \sqrt{ R^2 ~+~ \left( \omega \, L ~-~ \frac{1}{\omega \, C} \right)^2 } $$

Thus, we can also write the maximum current as follows:$$ I_0 ~=~ \frac{ U_0 }{ | Z | } $$

Peak voltage

Unit
Also the voltage \( U(t) \) oscillates periodically with time, but \(U_0\) represents the maximum value, i.e. the peak voltage. This can be, for example, the amplitude of the applied AC voltage.

Ohmic resistance

Unit
The ohmic resistance in the RLC series circuit. The larger the resistance, the smaller the maximum possible current \( I_0 \).

Inductance

Unit
The inductance of the coil in the RLC series circuit. Together with the angular frequency \( \omega \) it forms the inductive reactance: \( X_{\text L} = \omega \, L \).

Capacitance

Unit
The electrical capacitance of the capacitor in the RLC series circuit. Together with the angular frequency \( \omega \) it forms the capacitive reactance: \( X_{\text C} = - \frac{1}{ \omega \, C } \).

Angular frequency

Unit
The angular frequency describes indirectly by the relation \( \omega = 2\pi \, f \) with which frequency \( f \) the voltages at the \(R\), \(L\) and \(C\) elements and the current \(I\) change. This frequency is given by the applied AC voltage \( U(t) \).