Lab 6: R-C Circuits Only 6 more labs to go!! A capacitor is a device used to store energy. In this lab we will measure how a capacitor “stores” up or discharges energy. If we use Kirkchoff’s loop rule to the circuit below we get the following equation: CR V applied Switch Remember the definition of current is: So the equation becomes: This equation is called a differential equation. The solution to this differential equation is: This tells us that the charge on the capacitor is exponential in time.

Charge, Q time (s) Q = CV applied Since we now know how the capacitor charges up we can write an equation that describes the voltage as a function of time: t = RC =   C is called the RC-time constant. It represents the time which the voltage drop across the capacitor reaches 63% of it’s max value. Voltage, V time (s) t = RC = 

C = 5  FR = 10 5  V applied = 12 V Switch Let’s look at this example: 1. Find the time constant,  C. 2. Find the charge on the capacitor at t = 0.2 sec 3. Find the voltage on the capacitor at t = 0.3 sec 4. How long will it take the capacitor to charge to 9V?

Now we will look at how the capacitor discharges its energy. Let’s look at this circuit: Use Kirchoff’s loop: CR Switch The solution to this differential equation is: If we take the derivative of this equation with respect to time we can get the current: Charge, Q time (s)

C=5  FR=10 5  Switch V applied = 9V 1.Find the voltage across the capacitor at time, t = 0.3 s. 2. How long will it take the capacitor to reach 3 v?