The problem couldn't fit in the title so I'll put it here:
The problem below 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)
R dq/dt + q/C = V
where R, C, and V are constants.
(a) Solve for q(t), assuming that q(0) = 0.
(b) Show that lim t→∞ q(t) = CV.
(c) 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).
Негізгі бет AP Calculus: Differential Equation Word Problem
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