In an RC electrical circuit, the charge Q(t) (in coulombs) on a capacitor at time t seconds satisfies
dtdQ=0.02(100−Q).
\nInitially the capacitor is uncharged, so Q(0)=0.
a. Solve the differential equation to obtain Q(t).
b. Determine the time required for the charge on the capacitor to reach 80 C. Express your answer to the nearest tenth of a second.
c. Find the current I(t)=dtdQ at the time calculated in part (b), and include appropriate units.
d. State the limiting charge as t→∞ and interpret this value in the context of the circuit.