?Charging a capacitor A capacitor is a device that stores electrical charge. The charge

Chapter 6, Problem 33

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

a. Graph the charge function for \(t \geq 0\) using a = 1 and c = 10. Find a graphing window that shows the full range of the function.

b. Vary the value of a holding c fixed. Describe the effect on the curve. How does the steady-state charge vary with a?

c. Vary the value of c holding a fixed. Describe the effect on the curve. How does the steady-state charge vary with c?

d. Find a formula that gives the steady-state charge in terms of a and c.