Chapter 3.5, Problem 6E

6. Derive a power balance equation for the RL and RC circuits. (see Problem 5) Discuss the significance of the signs of the three power terms.

5. The power generated or dissipated by a circuit element equals the voltage across the element times the current through the element. Show that the power dissipated by a resistor equals $I^{2}R$, the power associated with an inductor equals the derivative of $\frac{1}{2}L{I}^2$, and the power associated with a capacitor equals the derivative of $\frac{1}{2}C{E}_C^2$.