# LC VOLTAGE

<p class="callout info">The impedance of an inductor and a capacitor in series, <span class="katex">**<span class="katex-mathml">Z<sub>series</sub></span>**<span aria-hidden="true" class="katex-html"><span class="base"><span class="mord"><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist-s">​</span></span></span></span></span></span></span></span>, is given by</p>

[![image-1729955826232.png](https://stanslegacy.com/uploads/images/gallery/2024-10/scaled-1680-/e2oPL6lIsE05xsc8-image-1729955826232.png)](https://stanslegacy.com/uploads/images/gallery/2024-10/e2oPL6lIsE05xsc8-image-1729955826232.png)

> <span class="katex-display"><span class="katex"><span class="katex-mathml">Z<sub>series</sub> = (Xc−Xl)</span></span></span>

Where

> <span class="katex-display"><span class="katex"><span class="katex-mathml">Xc = 1 / 2(pi)FC</span></span></span>

The **Resonant Frequency (F)** of an LC circuit in series is given by

[![image-1729955988059.png](https://stanslegacy.com/uploads/images/gallery/2024-10/scaled-1680-/JBb9dYTJNfm7zqbn-image-1729955988059.png)](https://stanslegacy.com/uploads/images/gallery/2024-10/JBb9dYTJNfm7zqbn-image-1729955988059.png)

**Ohm’s Law** for an LC circuit in series is given by

> <span class="katex-display"><span class="katex"><span class="katex-mathml">V<sub>t</sub> = IZ</span></span></span>

### LC VOLTAGE

[![image-1729909194850.png](https://stanslegacy.com/uploads/images/gallery/2024-10/scaled-1680-/bz2ed0WefL8PK2ax-image-1729909194850.png)](https://stanslegacy.com/uploads/images/gallery/2024-10/bz2ed0WefL8PK2ax-image-1729909194850.png)The voltage across the **inductor** (c) <span style="text-decoration: underline;">or</span> **capacitor** (*ER of t*) is <span style="text-decoration: underline;">greater than</span> the **applied voltage** (h).

<p class="callout success">At frequency <span style="text-decoration: underline;">close to resonance</span>, the voltage across the individual components is higher than the **applied voltage** (h), and, at resonant frequency, <span style="text-decoration: underline;">the voltage <span class="katex"><span class="katex-mathml">VT</span><span aria-hidden="true" class="katex-html"><span class="base"><span class="mord"><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist-s">​</span></span></span></span></span></span></span></span> across both the inductor and the capacitor are theoretically infinite</span>.</p>

<p class="callout warning">However, physical constraints of components and circuit interaction prevent the voltage from reaching infinity.</p>

The **voltage** (<span class="katex"><span class="katex-mathml">V<sub>L</sub></span><span aria-hidden="true" class="katex-html"><span class="base"><span class="mord"><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist-s">​</span></span></span></span></span></span></span></span>) across the **inductor** (C) is given by the equation:

<span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="mord"><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="msupsub"><span class="vlist-s">​</span></span></span><span class="vlist-s">​[![image-1729955839529.png](https://stanslegacy.com/uploads/images/gallery/2024-10/scaled-1680-/9BnePcClfpCv9QQf-image-1729955839529.png)](https://stanslegacy.com/uploads/images/gallery/2024-10/9BnePcClfpCv9QQf-image-1729955839529.png)</span></span></span></span></span></span></span></span></span>