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Dynamics 11 Physics II online lab: Lab 2: Capacitors; Series and Parallel circuits Page # Name:____________________________________ Section: _______ Lab 2: Capacitors; Series and Parallel circuits In this activity you will use the Simulation: Capacitor Lab kit to develop your understanding of the capacitors characteristics, and series and parallel circuit analysis, charge and discharge of a resistor 1. Objective To study Capacitors, Conservation of energy, series and parallel circuit analysis. Students will be able to: · Identify the variables that affect the capacitance and how each affects the capacitance. · Determine the relationships between charge, voltage, and stored energy for a capacitor. · Relate the design of the capacitor system to its ability to store energy. · Determine the equivalent capacitance of a set of capacitors in series and in parallel in a circuit. · Determine the energy stored in a set of capacitors in a circuit. · Explore how varying the amount of dielectric material inserted between the conductors affects the function of the capacitor. · Explain how a capacitor or set of capacitors would be used in a real world application. · Explain how a capacitor discharges and what is the application in real world 2. Apparatus PhET online software for Capacitor 3. Theory 3.1. Capacitor characteristics A capacitor is a device for storing electric charge and energy. For simplicity, an ideal capacitor can be considered as a pair of parallel conducting metal plates, as shown in Fig. 1. The symbol is very similar to a battery with the difference that the two plates are equal while for the battery the positive is bigger than the negative. A polar capacitor is having + and – plates as shown in the figure with the negative plate being curved. Fig. 1: The schematic representation of a capacitor and a polar capacitor (left) and a battery (right). When a charge +Q is placed on the upper plate and −Q on the lower plate, a potential difference V is established between the plates, and the quantities Q and V are related by the expression: (1) where the capacitance C is determined by the size and separation of the plates. Capacitance is a constant of proportionality. It relates the potential difference V between two conductors to their charge, Q. The charge Q is equal and opposite on the two conductors. The capacitance C of any two conductors depends on their size, shape, and separation. One of the simplest configurations is a pair of flat conducting plates, which is called a “parallel-plate capacitor.” Theoretically, the capacitance of parallel-plate capacitors is (2) where, A is the area of one of the plates, d is the distance between them, and is a constant called the “permittivity of free space,” which has a value of 8.85 × 10-12 C2 / N-m2 , in SI units. The unit of capacitance in SI is Farad which is a very large unit. A one FARAD capacitor would be the size of a car if made with plates and paper. For that reason most capacitances available on market are in the range of micro Farad(µF) to pico Farad pF) (10-6 - 10-12F). The capacitance C of the parallel plates depends on the medium inserted between the plates. When there is not a vacuum between the two capacitor plates, the capacitance in Eq. (2) should be re-written as (3) where K is the (dimensionless) dielectric constant of the material between the electrodes. Here is a table for some materials: As you can see, although we have been neglecting the dielectric constant of air, the error we make in doing so is quite small. You might ask whether you could make more measurements in this experiment, using materials other than air. If you like, as a test you may try inserting a book or a stack of paper between the electrodes, after you have charged them. The potential across the electrodes should diminish. Books with glossy covers don’t work well, because they are easily charged by handling them. A book with a rough cloth cover works well. 3.2. Electric field strength In a simple parallel-plate capacitor, a voltage applied between two conductive plates creates a uniform electric field between those plates. The electric field strength (E) in a capacitor is directly proportional to the voltage applied and inversely proportional to the distance between the plates as it is shown below: (4) Where V is the voltage and d is the distance between the two plates. This factor limits the maximum rated voltage of a capacitor, since the electric field strength must not exceed the breakdown field strength of the dielectric used in the capacitor. If the breakdown voltage is exceeded, an electrical arc is generated between the plates. This electric arc can destroy some types of capacitors instantly. The standard unit used for electric field strength is volts per meter [V/·m]. 3.3. Energy stored on a capacitor Capacitors are devices which are used to store electrical energy in a circuit. The energy supplied to the capacitor is stored in the form of an electric field which is created between the plates of a capacitor. When the voltage is applied across a capacitor, a certain amount of charge accumulates on the plates. The energy stored on the capacitor is: (5) where U is the energy stored, C is the capacitance and V is the voltage applied across the capacitor. 3.4. Types of capacitors There are two main types of capacitor. Ceramic capacitors and Electrolytic capacitors Fig. 2. Two main capacitor type and the method to read the capacitance Nearly all small capacitors are ceramic capacitors as this material is cheap and the capacitor can be made in very thin layers to produced a high capacitance for the size of the component. Capacitors from 1 pF to 100 nF are non-polar and can be inserted into a circuit around either way. Capacitors from 1µF to 100,000µF are electrolytics and are polarised. They must be fitted so the positive lead goes to the supply voltage and the negative lead goes to ground (or earth). There are many different sizes, shapes and types of capacitor. They are all the same. They consist of two plates with an insulating material between. The two plates can be stacked in layers or rolled together. The important factor is the insulating material. It must be very thin to keep things small. This gives the capacitor its VOLTAGE RATING. If a capacitor sees a voltage higher than its rating, the voltage will "jump through" the insulating material or around it. If this happens, a carbon deposit is left behind and the capacitor becomes "leaky" or very low resistance, as carbon is conductive. 3.5. Capacitors in series configuration When we build a circuit with capacitors, we can connect them in general in one of two ways: in series or in parallel. The way two capacitors are in series is sketched in Fig. 3. When two capacitors connected in series, i.e., in a line such that the positive plate of one is attached to the negative plate of the other--see Fig. 3. In fact, let us suppose that the positive plate of capacitor 1 is connected to the ``input'' wire, the negative plate of capacitor 1 is connected to the positive plate of capacitor 2, and the negative plate of capacitor 2 is connected to the ``output'' wire Fig. 3: The schematic representation of a capacitor showing two capacitors in series. In this case, it is important to realize that the charge Q stored in the two capacitors is the same. This is most easily seen by considering the ``internal'' plates: i.e., the negative plate of capacitor 1, and the positive plate of capacitor 2. These plates are physically disconnected from the rest of the circuit, so the total charge on them must remain constant. Assuming, as seems reasonable, that these plates carry zero charge when zero potential difference is applied across the two capacitors, it follows that in the presence of a non-zero potential difference the charge +Q on the positive plate of capacitor 2 must be balanced by an equal and opposite charge –Q on the negative plate of capacitor 1. Since the negative plate of capacitor 1 carries a charge -Q, the positive plate must carry a charge +Q. Likewise, since the positive plate of capacitor 2 carries a charge +Q, the negative plate must carry a charge -Q. The net result is that both capacitors possess the same stored charge Q. The potential drops, V1 and V2, across the two capacitors are, in general, different. However, the sum of these drops equals the total potential drop V applied across the input and output wires: i.e., V=V1+V2. The equivalent capacitance of the pair of capacitors is again Ceq =Q/V. Thus, The net capacitance for the series capacitors is given by the following expression (6) where Ceq will be less than either of the two resistances making up the parallel combination. For many capacitors in parallel, the equation becomes: and, once again, Ceq will be less than the smallest capacitor in the combination. 3.6. Capacitors in parallel configuration For a parallel configuration, the capacitors look like Fig. 4. When two capacitors are connected in parallel, with the positively charged plates connected to a common ``input'' wire, and the negatively charged plates attached to a common ``output'' wire--see Fig.4. Fig. 4: The schematic representation of two capacitors in parallel. What is the equivalent capacitance between the input and output wires? In this case, the potential difference V across the two capacitors is the same, and is equal to the potential difference between the input and output wires. The total charge Q, however, stored in the two capacitors is divided between the capacitors, since it must distribute itself such that the voltage across the two is the same. Since the capacitors may have different capacitances, C1 and C2, the charges Q1 and Q2 may also be different. The equivalent capacitance Qeq of the pair of capacitors is simply the ratio Q/V where Q = Q1 + Q2 is the total stored charge. It follows that - (7) Here, we have made use of the fact that the voltage V is common to all three capacitors. Thus, the rule is: The equivalent capacitance of two capacitors connected in parallel is the sum of the individual capacitances. Putting two capacitors in parallel makes the net (equivalent) capacitance, the sum of the capacitors: Ceq = C1 + C2, or in general for many capacitors Ceq = C1 + C2 + C3 + · + CN (8) for a total of N capacitors in series. 3.7. Mixed configuration