Electric energy

Electric potential energy

$U_E=k\frac{q_1{q}_2}{r}$

• Electric potential energy is the energy stored in a system of charges due to their positions relative to each other
• The work done in bringing a charge from infinity to that point
• $U_{\mathrm{E}}(\mathbf{r})=-W_{r_{\mathrm{ref}}\to r}=-{\int }_{{\mathbf{r}}_{\mathrm{ref}}}^{\mathbf{r}}q\mathbf{E}({\mathbf{r}}^{\prime })\cdot \mathrm{d}{\mathbf{r}}^{\prime }$

Electric energy

• Electric energy is the capacity to do work
• $E={\int }_{t_0}^{t}Pdt={\int }_{t_0}^{t}VIdt$
  • $E$ is electrical energy (in joules) absorbed or supplied by an element from time $t_0$ to time $t$
  • $P$ is power (in watts)
  • $V$ is voltage (in volts)
  • $I$ is current (in amperes)