Remarks
- Good approximation for metals. A material that obeys Ohm’s law is called Ohmic. Many are non-Ohmic (like diodes)
- $\rho$ is called resistivity, measured in $(\mathrm{V} / \mathrm{m}) /\left(\mathrm{A} / \mathrm{m}^{2}\right)=\mathrm{V} \cdot \mathrm{m} / \mathrm{A}=\Omega \cdot\mathrm{m}$. It characterizes the intrinsic resistance to a electric current. Same symbol as volume density charge, do not confuse them!!!
- The reciprocal of resistivity is conductivity.
- Poor electrical conductors (ceramics, plastics) are normally poor thermal conductors as well, as particles are nor free to transport any form of energy. ![[Pasted image 20240306171835.png]]
#Resistance
Ohm’s law can be re-expressed in a more convenient form. Let’s assume the conductor is a long wire of length $L$ and cross-section area $A$. Let $V$ potential difference between the extremes of the wire, and $I$ the current flowing within. As $\vec J$ and $\vec E$ are constant and parallel along the wire, we can write $I=JA$ and $V=EL$, hence
$$ V=\frac{\rho L}{A} I=RI $$Properties
- $R=V/I$ is called resistance, measured in Ohms ($\Omega=V/A$). Unlike the resistivity, it is not an intrinsic quantity of the material as it also depends on the geometry.
- Typical values in circuits $\Omega$, kilohms, $k\Omega=10^{3}\Omega$, megaohms $M\Omega=10^{6}\Omega$
- Resistance varies with temperature, the simples model is linear $R(T)\approx R_{0}\left[1+\alpha\left(T-T_{0}\right)\right]$.
- A circuit component made to have a specific value of resistance is called a resistor.
In practice, real resistors of different values are used to limit the current in a certain part of the circuit. ![[Pasted image 20240306171842.png]]
Mutual Inductance