My name is Alexander Fufa

**eV**and here I will explain the following topic:# RLC Series Circuit

## Formula

## What do the formula symbols mean?

## Impedance

`$$ |Z| $$`Unit

`$$ \mathrm{\Omega} $$`

Impedance is the magnitude of the complex resistance \( Z \). This formula gives the total impedance of a resistor-coil-capacitor series circuit (RLC series circuit). To obtain this formula, the Pythagorean theorem was applied to a phasor diagram on which the three quantities are plotted:

**Ohmic impedance**: \(Z_{\text R } ~=~ R \).**Inductive impedance**: \(Z_{\text L } ~=~ \text{i} \, \omega \, L \).**Capacitive impedance**: \(Z_{\text C } ~=~ -\text{i}\frac{1}{\omega \, C} \).

## Inductance

`$$ L $$`Unit

`$$ \mathrm{H} = \frac{ \mathrm{Vs} }{ \mathrm{A} } $$`

The inductance of the coil connected to the RLC circuit.

## Capacitance

`$$ C $$`Unit

`$$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$`

Capacitance of the capacitor connected to the RLC circuit.

## Electrical Resistance

`$$ R $$`Unit

`$$ \mathrm{\Omega} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A}^2 \, \mathrm{s}^3 } $$`

Ohmic resistance of a resistor connected to the RLC series circuit.

## Angular frequency

`$$ \class{green}{\omega} $$`Unit

`$$ \frac{\mathrm{rad}}{\mathrm s} $$`

The angular frequency \( \omega = 2\pi \, f \) indicates the frequency \(f\) at which the LRC circuit oscillates. The frequency \(f\) is specified, for example, by the frequency of the applied AC voltage.

**Explanation**

## Video

An RLC series circuit consists of a resistor \( R \), an inductor \( L \) and a capacitor \( C \), which are arranged in series in an electrical circuit. These components form a series of consecutive elements through which the current can flow.

Formula anchor
$$ \begin{align} |Z| ~=~ \sqrt{ R^2 ~+~ \left( \class{green}{\omega} \, \class{brown}{L} ~-~ \frac{1}{\class{green}{\omega} \, \class{purple}{C}} \right)^2 } \end{align} $$

Formula anchor
$$ \begin{align} \tan(\varphi) ~=~ \frac{ \class{green}{\omega} \, \class{brown}{L} ~-~ \frac{1}{\class{green}{\omega} \, \class{purple}{C}} }{ R } \end{align} $$

Formula anchor
$$ \begin{align} I_0 ~=~ \frac{ U_0 }{ \sqrt{ R^2 ~+~ \left( \class{green}{\omega} \, \class{brown}{L} ~-~ \frac{1}{\class{green}{\omega} \, \class{purple}{C}} \right)^2 } } \end{align} $$