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Electric current

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  • Ohm's law for an inhomogeneous segment of a circuit:$$ I=\frac{V_{12}}{R}=\frac{\phi_{1}-\phi_{2} + \mathscr{C}_{12}}{R} $$  where $V_{12}$ is the voltage drop across the segment.
  • Differential form of Ohm's law:$$ j=\sigma (E + E*),$$ where $E^*$ is the strength of a field produced by extraneous forces.
  • Kirchhoff's laws (for an electric circuit):$$ \sum I_k=0, \sum I_k R_k= \sum \mathscr{C}_k .$$
  • Power P of current and thermal power Q:$$P=VI=(\phi_1 - \phi_2 +\mathscr{C}_{12})I, Q=RI^2.$$
  • Specific power $P_{sp}$ of current and specific thermal power $Q_{sp}$:$$P_{sp}=j(E+E^*), Q_{sp}=\rho j^2 $$
  • Current density in a metal:$$j=enu,\tag{6}$$ where u is the average velocity of carriers.
  • Number of ions recombining per unit volume of gas per unit time:$$n_r=rn^{2}\tag{7}$$ where r is the recombination coefficient.

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