Peoples Physics Concepts

15.4. RC Time Constant http://www.ck12.org

15.4 RC Time Constant

• Define the RC time constant and solve various problems involving resistor-capacitor circuits.

Students will learn about the RC time constant and how to solve various problems involving resistor-capacitor

circuits.

Key Equations

Q(t) =Q 0 e

−τt

Discharge rate, whereτ=RC

I(t) =I 0 e

−τt

Electric current flow varies with time in a like manner

Guidance

When a capacitor is initially uncharged, it is very easy to stuff charge in. As charge builds, it repels new charge with

more and more force. Due to this effect, the charging of a capacitor follows a logarithmic curve. When you pass

current through a resistor into a capacitor, the capacitor eventually “fills up” and no more current flows. A typical

RC circuit is shown below; when the switch is closed, the capacitor discharges with an exponentially decreasing

current.

Example 1

In the circuit diagram shown above, the resistor has a value of 100Ωand the capacitor has a capacitance of 500μF.
After the switched is closed, (a) how long will it be until the charge on the capacitor is only 10% of what it was
when the switch was originally closed? If the capacitor was originally charged by a 12 V battery, how much charge
will be left on it at this time?

Solution

(a): To solve the first part of the problem, we’ll use the equation that gives charge as a function of time.