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

## Peak current

`\( I_0 \)`Unit

`\( \mathrm{A} \)`

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

`\( U_0 \)`Unit

`\( \mathrm{V} \)`

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

`\( R \)`Unit

`\( \mathrm{\Omega} \)`

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

## Inductance

`\( L \)`Unit

`\( \mathrm{H} \)`

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

`\( C \)`Unit

`\( \mathrm{F} \)`

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

`\( \omega \)`Unit

`\( \frac{1}{\mathrm s} \)`

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 \( U(t) \).