# Dictionary:State variable

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One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation:

${\displaystyle E(t)=RI+L{\frac {dI}{dt}}+C\int _{t}Idt}$.

Using state variables of ${\textstyle I}$, ${\textstyle Q=\int Idt}$, and ${\textstyle P={\frac {dI}{dt}}}$ permits this to be written as a set of three simultaneous equations:

${\displaystyle E(t)=RI+LP+CQ}$,

${\displaystyle {\frac {dQ}{dt}}=I}$, and

${\displaystyle {\frac {dI}{dt}}=P}$.