Figure 13 shows a circuit consisting of a resistor of R ohms, a capacitor of C farads, and a battery of voltage V. When the circuit is completed, the amount of charge q(t) (in coulombs) on the plates of the capacitor varies according to the differential equation (t in seconds)

where R, C, and V are constants.
(a) Solve for q(t), assuming that q(0) = 0.
(b) Sketch the graph of q.

(c)

(d) Show that the capacitor charges to approximately 63% of its final value CV after a time period of length τ = RC (τ is called the time constant of the capacitor).

Transcribed Image Text:

dq R- dt + 1 C q=V