Capacitors (0430)

Charge on Capacitors

We set up a closed circuit to charge a capacitor. We then used the charged capacitor to light a bulb without the batteries in the circuit. We measured how long it took for the bulb to go completely unlit and graphed our results.

Capacitor discharge.

Voltage cross fully charge the capacitor.

In this photo, we draw a sketch of the brightness of the bulb and the time when it is placed across a charged capacitor without the battery present. 

It is a non-line graph. at first, the time is 0, the bulb is most brightness, then as time increases, the bulb gets dimer and dimer.

Here, we tried to obtain the 5uF capacitor by combining five 1uF capacitor in parallel.

 

The red curve represents the charging capacitor, voltage goes up over the course of time. While the blue curve represents the discharging the capacitor, the voltage drops over the course of time. The equation we used for the curve fit is y=A^(1-exp(-Ct))+B for both curves. Interestingly, the C are the same for both graphs, which implying that C is a constant, we found that C is actually 1/Tau=1/RC (R, C are constants, therefore Tau has to be constant)

Here we were trying to find the unit of Tau, to prove that Tau is actually R*C.

After we found the unit of Tau, we set up the equation Q/C= I*R. Since I=dq/dt. We can integrate both side dq/q=dt/Tau. The result is the last equation we wrote on the board.

We said that brightness can be understood as power. Since I=dq/dt=d(CV)/dt)= C*dV/dt. We can see that I graph would be the derivative of voltage graph

Finding Q max here. since Q=V*C= 4.5*e^(-t*C). Q will be max  when t=0, which then equals to 0.45 C

Summary:

     In today’s class, we analyze the idea of capacitors and the charge buildup and discharging of capacitors in a circuit. We did many experiments on capacitors to understand how they work, and how they affect a circuit. We know that what happens when connected in series or parallel, and we did experiments at the different types of RC circuits about developing a relationship between their charging and discharging.  At the end of the class we did some excises to calculate capacitance, time constants, and maximum charge of a circuit