Chapter 1.3, Problem 80E

Charging a capacitor A capacitor is a device that stores electrical charge. The charge on a capacitor accumulates according to the function Q(t) = a(1 − e^−t/c), where t is measured in seconds, and a and c > 0 are physical constants. The steady-state charge is the value that Q(t) approaches as t becomes large.

1. a. Graph the charge function for t ≥ 0 using a = 1 and c = 10. Find a graphing window that shows the full range of the function.
2. b. Vary the value of a while holding c fixed. Describe the effect on the curve. How does the steady-state charge vary with a?
3. c. Vary the value of c while holding a fixed. Describe the effect on the curve. How does the steady-state charge vary with c?
4. d. Find a formula that gives the steady-state charge in terms of a and c.