# PDE: Why do they have the wrong units?

Take a look, for example, at the telegrapher's equations (let's look at the voltage one). They have the wrong units.

Equation

$u_{x} = Li_{t} + Ri$

*where $u$ is potential in volts $V$, $L$ is inductance in henries $H$, $i$ is current in amperes $A$, $R$ is resistance in ohms $\Omega$.

Unit Analysis

$[\frac{V}{m}] = [V]$

This appears to be consistent across many PDEs. What am I missing?

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I don't understand your “unit analysis”. What are $V$ and $M$? – Harald Hanche-Olsen May 10 '13 at 19:32
Post modified... – nick_name May 10 '13 at 19:35
$L, R$ should be 'per unit length' quantities. $u$ should be in volts, and $i$ in amps. – copper.hat May 10 '13 at 19:36
Oh, I get it. $V$ is supposed to mean Volts, and $M$ is meters? But meters are written with a lowercase m. – Harald Hanche-Olsen May 10 '13 at 19:36
@copper.hat So are you implying that in all PDEs where the units appear off, that the multiplicative constants must be dimensionally normalized? – nick_name May 10 '13 at 19:38

The units are fine. $L$ is inductance per length unit and $R$ is resistance per length unit.