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?

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