Electric current

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Ohm's law for an inhomogeneous segment of a circuit:$$ I=\frac{V_{12}}{R}=\frac{\phi_{1}-\phi_{2} + \mathscr{E}_{12}}{R},$$ where $V_{12}$ is the voltage drop across the segment.
Differential form of Ohm's law:$$\vec{j}=\sigma (\vec{E} + \vec{E}^\star),$$ where $\vec{E}^\star$ is the strength of a field produced by extraneous forces.
Kirchhoff's laws (for an electric circuit): $$ \sum I_k=0, \sum I_k R_k= \sum \mathscr{E}_k.$$
Power P of current and thermal power Q: $$P=VI=(\phi_1 - \phi_2 +\mathscr{E}_{12})I, Q=RI^2.$$

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Ohm's law for an inhomogeneous segment of a circuit:$$ I=\frac{V_{12}}{R}=\frac{\phi_{1}-\phi_{2} + \mathscr{E}_{12}}{R},$$ where $V_{12}$ is the voltage drop across the segment.
Differential form of Ohm's law:$$\vec{j}=\sigma (\vec{E} + \vec{E}^\star),$$ where $\vec{E}^\star$ is the strength of a field produced by extraneous forces.
Kirchhoff's laws (for an electric circuit): $$ \sum I_k=0, \sum I_k R_k= \sum \mathscr{E}_k.$$
Power P of current and thermal power Q: $$P=VI=(\phi_1 - \phi_2 +\mathscr{E}_{12})I, Q=RI^2.$$
Specific power $P_{sp}$ of current and specific thermal power $Q_{sp}$: $$P_{sp}=\vec{j}.(\vec{E}+\vec{E}^\star), Q_{sp}=\rho \vec{j}^2.$$
Current density in a metal: $$\vec{j}=en\vec{u},$$ where \$vec{u}$ is the average velocity of carriers.
Number of ions recombining per unit volume of gas per unit time:$$\dot{n}_r=rn^{2},$$ where $r$ is the recombination coefficient.