Adding LaTeX Equations
We have enabled the LaTeX markdown extensions using MathJax on this site. There are three ways to render eqations:
- Inline: simply surround the LaTeX expression with dollar signs
- Centered: surround the LeTex expression with '''[''' and ''']'''
- Block: place double dollar signs on a separate line before and after the LaTeX expression
Rendering Ohm's Law in Markdown
Here is an inline equation rendering of Ohm's Law: \(V=IR\).
$V=IR$
This example is centered:
\[ V = IR \]
\[ V = IR \]
\[
V=IR
\]
$$
V=IR
$$
The Shockley Diode Equation
The Shockley diode equation describes the current–voltage relationship of a diode:
\[
I = I_S \left( e^{\frac{V}{n V_T}} - 1 \right)
\]
where:
- \( I \) is the diode current,
- \( I_S \) is the reverse saturation current,
- \( V \) is the voltage across the diode,
- \( n \) is the ideality factor,
- \( V_T \) is the thermal voltage, \( V_T = \dfrac{k T}{q} \).
$$
I = I_S \left( e^{\frac{V}{n V_T}} - 1 \right)
$$
where:
- \( I \) is the diode current,
- \( I_S \) is the reverse saturation current,
- \( V \) is the voltage across the diode,
- \( n \) is the ideality factor,
- \( V_T \) is the thermal voltage, \( V_T = \dfrac{k T}{q} \).
Voltage Across a Capacitor
The voltage across a capacitor at any given time is determined by the history of the current that has flowed through it. We can express this as the sum of the initial voltage plus a integral of the current over time.
\[
v(t) = v(t_0) + \frac{1}{C} \int_{t_0}^{t} i(t)dt
\]
where:
- \(v(t)\): Voltage across the capacitor at time \(t\)
- \(v(t_0)\): Initial voltage across the capacitor at time \(t_0\)
- \(C\): Capacitance (in farads)
- \(i(t)\): Current flowing through the capacitor at time \(t\)
- \(t_0\): Initial time (often taken as t=0)
v(t) = v(t_0) + \frac{1}{C} \int_{t_0}^{t} i(t)dt
Other Examples
And here is a display equation that includes an integral, infinity, an exponent, a square, and square root and the symbol for \(\pi\):
\[
\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
\]
\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
\[
\operatorname{ker} f=\{g\in G:f(g)=e_{H}\}{\mbox{.}}
\]
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