Dielectrics and Dielectric Constant

capacitors are very useful devices as they allow us to store electric potential energy within the electric field that is created as a result of a separation of electric charge so let's begin by looking at these two diagrams that have parallel plate capacitors so in diagram a we have a parallel plate capacitor and we also have a battery now the battery essentially acts to charge our parallel plate capacitor and when that capacitor is fully charged it looks something like this so one of the plates has a negative charge the other plate has a positive charge now because they are separated by certain distance that means we have a separation of electric charge and that will create an electric field midway or in between our two plates and we can then store electric potential energy within that electric field which then can be used to do useful work for example power a computer or phone now the gap separating the two plates of the capacitor contains air and generally speaking air acts as an insulating material and that means it prevents electrons from flowing from this region to this region now the problem with using air is the following at very high voltages what happens is air becomes ionized the air molecules lose electrons and that essentially allows the electrons from this plate to flow to this plate and we essentially have a loss of separation of charge and that destroys our capacitor so once again the problem with using air is that at high enough voltages the air molecules become ionized and they begin conducting electrons across the plate so at low voltages the air is a good insulator but at high voltages it becomes ionized and allows electrons to flow from this plate to this plate this our capacitor now one way that we can tackle this problem is by replacing air with another type of insulating material that is capable of withstanding high voltages and this insulating material is usually called a dielectric so we can place some type of dielectric in between our two plates now let's examine what the effects are of placing a dielectric between our two plates so one thing that a dielectric does to a capacitor is it increases the capacitance it increases the quantity of electric charge that can be stored on either one of our plates so there are two ways that we can increase our capacitance so one way is we can bring our plates closer so now that we have a very thin sheet of dielectric between our two plates we can bring our plates closer thereby decreasing our distance between our two plates because our capacitance is universally proportional to our distance if we decrease our distance we increase our capacitance now even if our distance between the two plates remains the same the dielectrics will still increase our capacitance by a factor of K which is usually determined via experiment now K is known as the dielectric constant and it's actually depends on the type of substance that we are using so different substances will have different K values now what this basically means is the following if we define our C naught as the capacitance when the space in between our two plates is a vacuum then we see that our capacitance C with our dielectric is equal to C naught multiplied by this factor of K now recall that C naught the capacitance when the space between is a vacuum is equal to the product of the permittivity of free space epsilon naught multiplied by the surface area of either one of these plates divided by the distance separating our two plates so we can take this equation and replace C naught with this ratio and we get this result so the capacitance with our dielectric is equal to the product of the dielectric constant K the permittivity of free space given by epsilon naught the surface area of either one of the plates divided by the separation distance between our two plates so if we now define a new constant given by epsilon to be the product of K and epsilon naught then we have the following equation so the capacitance of our parallel plate capacitor width the dielectric in-between is equal to epsilon multiplied by a divided by D where our epsilon is known as the permittivity of our dielectric material that we are using so once again epsilon is a constant it's the product of the dielectric constant and our permittivity of free space now let's move on to the second effect dielectrics also increase the charge stored on our capacitive and that makes sense because if our capacitance increases our capacity by definition of capacitance is now able to store more electric charge so let's see what that means by looking at the following equations so recall that the quantity of electric charge that can be stored on our plate when there is a vacuum in between is equal to C naught our capacitance when there's a vacuum in between multiplied by the voltage difference so Q is equal to C multiplied by V now if we take this equation rearrange it and solve for C naught we see that C naught is equal to C divided by K so let's replace C naught with C divided by K so now we have this equation we can take K bring it to this side we get this result the product of the capacitance of our dielectric capacitor multiplied by the voltage is equal to K multiplied by Q naught so this is simply equal to Q the quantity of electric charge stored on our capacitor when there is a dielectric in between this is equal to cv which is equal to K multiplied by Q naught so we see Q the quantity of charge that is stored on our capacitor with a dielectric is equal to K the dielectric constant multiplied by Q naught so let's move on to the third effect that our dielectric has on our parallel plate capacitor so dielectrics decrease the voltage so the voltage between our two plates when there's a dielectric in between is equal to V naught divided by K where V naught is the voltage between our two plates when there's a vacuum in between so we see with the dielectric the voltage drops by a factor of K so capacitance increases by a factor of K the charge increases by a factor of K and our voltage drops by a factor of K now because voltage also depends on electric field we see that if the voltage drops the electric field also decreases between our two parallel plates so we see in effect number for the dielectrics decrease the electric field so let's look at the case without our dielectrics so without dielectrics we see that the electric field E naught is equal to V naught divided by D so the electric field is constant now with dielectrics our electric field which is just given by our E is equal to the voltage between our two plates with a dielectric divided by D now from this part we know voltage is two V naught divided by K so if we replace our voltage with V naught divided by K we get this result so we see that the electric field between our plates with our dielectric is equal to e naught divided by K so not only will the voltage decrease by a factor of K our electric field will also decrease by a factor of K so once again capacitance increases by a factor of K the charge increases by a factor of K the voltage decreases by a factor of K and electric field also decreases by a factor of K between our two parallel plates within this capacitor

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Keywords: dielectric, dielectric constant, effects of dieletric, capacitance and dielectric, voltage and dielectric, electric field and dielectric, physics, lectures, physics lectures

Id: yUQyCd4eF_I

Length: 9min 38sec (578 seconds)

Published: Fri Nov 29 2013