# Interesting Relationship

A series RC (resistor-capacitor) circuit is energized by an ideal DC voltage source through a switch that closes at time $$t = 0$$. The capacitor is initially uncharged.

For this example, $$V = 5$$, $$R = 2$$, and $$C = 3$$ (all in SI units).

Let $$E_R$$ be the total energy dissipated in the resistor from $$t = 0$$ to the present time. Let $$E_C$$ be the energy stored in the capacitor at the present time. Consider the following quantities:

• $$A$$ = the limiting value of $$E_R$$ as $$t$$ approaches $$\infty$$
• $$B$$ = the limiting value of $$E_C$$ as $$t$$ approaches $$\infty$$.

Which statement is true?

×