Charging And Discharging Capacitors

Purpose:  We attempt to find whether capacitors achieve the potential of the power supply instantaneously or if it takes some amount of time for the capacitor to charge. For this, we utilize Logger Pro to see the behavior of potential as a function of time.

Seeing How Capacitors Charge

To begin, we create a circuit with a power supply, a light bulb, and a capacitor. When all are connected, the light bulb shows no light. This is because the circuit is not completed, as there is a break within the capacitor. This break causes no current to flow. But, what we end up seeing, after time has passed, is that when we disconnect the power supply and only connect the capacitor with the light bulb, the bulb lights up and then begins to dim. This means that the capacitor charged while connected to the power supply which makes sense because we have negative charge gathering at one end of the capacitor and positive at the other end, essentially creating a new power supply. But how fast does a capacitor charge?



We made predictions for the potential of a capacitor and found that we over estimated the potential.

How Fast Does It Charge

When we graph the potential vs. time of the capacitance, we see that the potential increase exponentially.

Charging Rate Of Capacitors

We hook up a new capacitor to a circuit and connect the capacitor to Logger Pro so that we can examine how the potential changes exponentially.

Rate At Which A Capacitor Charges

As we look at how the capacitor charges, we fit the slope of the line with the closest fit equation which turns out to be some variation of the exponential function. We will later interpret what these values actually mean.

Rate At Which A Capacitor Discharges

We observe how a capacitor discharges and find the it goes at an exponential rate as well. The values of the function will, also, be later interpreted.

Deriving The Potential OF a Capacitor As A Function Of Time

We start off by looking at the general equation for capacitance and make it in terms of the potential. We also know that the potential is dependent on the current and the resistance. When we set these two potential equations equal, we solve for the charge. We know that current can be written as the change in q with respect to time. With a little algebra, we set up two integrals and solve for q. We get a definition for the charge of a capacitor with respect to time. Since the charge is proportional to the potential, we can rewrite this equation by replacing the charges with potentials. This gives us our function for potential with respect to time. This looks very similar to the fit equation found in Logger Pro.

How Long Does It Take For A Potential To Charge

We are given a circuit with a switch and when the switch is closed, the emf charges the capacitor. With the given values, we are able to solve for the time that it takes to charge the capacitor. This just involves using our derived formula and plugging in the values.

We take a look at the same problem, but we look at how long the capacitor takes to reach a charge of an electron. This just requires us to alter the potential equation so that it outputs a charge value.

Conclusion:  We find that capacitors take some time to attain potential as well as charge. We found that this time is dependent on an exponential function. As time passes, the capacitor charges quicker and quicker. The same can be said about discharging. There are slight differences between the equations for charge and discharge but the idea is the this occurs exponentially. When a capacitor is connected to a power supply, it charges, and we can then disconnect the power supply and use the capacitor as a new power supply. The only difference is that the power decreases.