Capacitors
Goal of the class Distinguish between electrical potential energy, electric potential, and potential difference. Solve problems involving electrical energy and potential difference. Question of the Day: What is the value of the electric field inside a conductor? Previous answer: No previous question Previous question: What is the value of the electric field inside a conductor?
Question The battery shown has a potential difference of 6.0 volts. It has just been connected to two metal plates separated by an air gap. There is no electrical connection between the two plates and air is a very poor conductor. If a light bulb replaced the two metal plates and the battery was connected, electrons would flow out of the negative and into the positive terminal. Will this also occur with the two metal plates? If not, why not? If so, is the flow similar or different from that with the light bulb? Explain. It is likely that students’ experience with capacitors is limited, so these questions may be confusing for them. The term capacitor is not introduced yet to reduce confusion. Try getting out a light bulb and connecting it to a battery. Discuss the flow of electrons from high PE (negative) to low PE (positive). Now replace the light bulb with parallel plates (or at least have students imagine the situation), and then move on to the second bullet point.
Capacitors The two metal plates are electrically neutral before the switch is closed. What will happen when the switch is closed if the left plate is connected to the negative terminal of the battery? Electrons are repelled from the negative terminal. As a result, they have high PE and flow toward the neutral plate. Eventually, as electrons build up on the plate, the PE of electrons on the plate equals that of the battery, and the flow stops. Similarly, electrons flow from the neutral right plate to a lower PE, the + terminal of the battery. Another explanation is that repulsion builds up between electrons on the left and right plates. This repulsion drives the electrons on the right plate to the battery terminal. + - Electrons will flow toward lower PE. From the battery to the left plate From the right plate to the battery
Parallel Plate Capacitors Capacitance is the ability of a conductor to store electrical energy by separating charges. Electrons build up on the left plate, giving it a net negative charge. The right plate has a net positive charge. Capacitors can store charge or electrical PE.
Capacitance Capacitance measures the ability to store charge SI unit: coulombs/volt (C/V) or farads (F) In what way(s) is a capacitor like a battery? In what way(s) is it different? Capacitors and batteries both have one terminal with excess electrons and another with a deficiency of electrons. They both store electrical PE. In both cases, electrons will flow from high PE to low PE when the two terminals are connected with a conductor. Capacitors, however, do not have the ability to maintain the PE difference or voltage between the terminals. Batteries use chemical energy to maintain the difference in charge (or energy) between the two terminals.
Capacitance How would capacitance change if the metal plates had more surface area? Capacitance would increase. How would it change if they were closer together? This equation is discussed further on the next slide.
Capacitance is a constant that is determined by the material between the plates (0 refers to a vacuum). Combining the two equations for C yields: This comes from Q=CV
Dielectrics The space between the plates is filled with a dielectric. Rubber, waxed paper, air The dielectric increases the capacitance. The induced charge on the dielectric allows more charge to build up on the plates. The better dielectrics are those that have charges induced on their surface more easily. This charge reduces the electric field between the plates, so more electrons can build up. The induced positive charge negates some of the repulsive force for the incoming electrons toward the top plate, so more electrons can build up on the top plate.
Capacitor Applications Connecting the two plates of a charged capacitor will discharge it. Flash attachments on cameras use a charged capacitor to produce a rapid flow of charge. Some computer keyboards use capacitors under the keys to sense the pressure. Pushing down on the key changes the capacitance, and circuits sense the change. For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful. Students do not need to use Coulomb’s law to calculate the answer to the second question. Felectric = Eq0 is much simpler. 6.62 10-6 C or 6.62 C 1.19 N for both test charge and object
Energy and Capacitors As the charge builds, it requires more and more work to add electrons to the plate due to the electrical repulsion. The average work or PE stored in the capacitor is (1/2)QV. Derive equivalent equations for PEelectric by substituting: Q = CV and V = Q/C The equivalent equations for PEelectric are: PEelectric = 1/2C(V)2 PEelectric = Q2/2C
Practice Problem A 225 F is capacitor connected to a 6.00 V battery and charged. How much charge is stored on the capacitor? How much electrical potential energy is stored on the capacitor? Answers: 1.35 x 10-3 C , 4.05 x 10-3 J These solutions are straightforward applications of the equations. Some of the units are new and unfamiliar to students, and this may present some problems.
Question If a light bulb replaced the two metal plates and the battery was connected, electrons would flow out of the negative and into the positive terminal. Will this also occur with the two metal plates? If not, why not? If so, is the flow similar or different from that with the light bulb? Explain. If a light bulb replaced the two metal plates and the battery was connected, electrons would flow out of the negative and into the positive terminal. Will this also occur with the two metal plates? If not, why not? If so, is the flow similar or different from that with the light bulb? Explain. It is likely that students’ experience with capacitors is limited, so these questions may be confusing for them. The term capacitor is not introduced yet to reduce confusion. Try getting out a light bulb and connecting it to a battery. Discuss the flow of electrons from high PE (negative) to low PE (positive). Now replace the light bulb with parallel plates (or at least have students imagine the situation), and then move on to the second bullet point.
Homework Please complete questions on page 616 Q 10, 13, 17-19