9 min read•january 8, 2023
Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
A capacitor is a device that can be used to store charge, and therefore, electrical potential energy. They are used in a wide range of electrical devices including the flash on your cell phone camera. There are several different ways to construct a capacitor, but we're going to focus on the parallel-plate version.
A capacitor is a device that stores electric charge and energy in an electric field. It consists of two conductors, called plates, separated by an insulating material called the dielectric.
Here are some key points about capacitors:
The parallel plate capacitor is created by taking two conductive plates and separating them by a small distance. A dielectric is often added to increase the amount of charge a capacitor can store. We'll discuss more about dielectrics in the next section.
Let's create a simple capacitor using two metal plates and connect them to a battery to charge them up. Recall from Unit 1, that the strength of the electric field is proportional to the amount charge. E=kQ/r^2
We also know that the potential difference (V) between the plates is related to the electric field through ΔV=Ed. Following this thought process, we can see that V∝Q as well. The more charge that gets stored on each plate, the stronger the field, and the higher the voltage between the plates will be. We'll define a new quantity, capacitance(C), as the constant of proportionality between V and Q such that:
The unit for capacitance is the Farad (F), where 1F =1C/1V
Let's derive what capacitance actually is. This derivation is beyond the course but will give you a deeper understanding of circuits.
We can also define capacitance in terms of the physical dimensions of the capacitor. Recall that σ=Q/A (area charge density) for a sheet of charge, and E=σ/ϵ0 for a conductive plate.
From here, we can see that capacitance is directly proportional to the area of the plates (A) and inversely proportional to the distance between them. This should make sense since a larger plate has more room for the charge to occupy and, therefore, more should be able to fit on it.
Because the capacitor stores charge, it also stores electric potential energy (UC). The amount of energy stored can be determined through a derivation. However, the derivation requires understanding of integral calculus we will just work with the final product.
Energy in a capacitor is the energy stored in the electric field between the capacitor plates. It is a measure of the potential energy of the electric charges stored on the capacitor plates.
Here are some key points about energy in a capacitor:
Take a few minutes and check out this Phet Simulation where you can alter the physical properties of a parallel plate capacitor and see the effect on voltage, field strength, and energy stored.
1. A 20 µF parallel-plate capacitor is fully charged to 20 V. The energy stored in the capacitor is most nearly __________.
2. A capacitor with circular parallel plates of radius R that are separated by a distance d has a capacitance of C. What would the capacitance (in terms of C ) be if the plates had radius 2R and were separated by a distance d/2 ?
The capacitance depends on the area of the plate, which for a circular plate is 2πr^2
Dielectrics are insulating materials that are often used in capacitors to increase their capacitance. They help solve the problem of how to get more charge into a capacitor without having the voltage decrease. C=Aϵo/d. Modifying the equation to include a dielectric involves adding a new term κ, which is the dielectric constant. In general, the easier a material is to polarize, the higher it's dielectric constant is. Values for common dielectrics are shown below:
Material | Dielectric Constant |
Vacuum | 1 |
Air | 1.00059 |
Bakelite | 4.9 |
Fused Quartz | 3.78 |
Neoprene Rubber | 6.7 |
Nylon | 3.4 |
Paper | 3.7 |
Polystyrene | 2.56 |
Pyrex Glass | 5.6 |
Silicon Oil | 2.5 |
Strontium Titanate | 233 |
Teflon | 2.1 |
Water | 80 |
Great question! It's because a dielectric becomes polarized easily. In fact, the easier the dielectric becomes polarized, the greater its κ becomes. Let's look at an image to understand why the polarization helps increase the capacitance.
In image (a), we can see that the molecules of the dielectric become polarized and align opposing the charge on the plates. This produces a layer of opposite charge on the surface of the dielectric that attracts more charge onto the plate, because of Coulomb's Law, increasing its capacitance.
Another way to understand how a dielectric increases capacitance is to look at how it changes the electric field inside the capacitor. Image (b) shows the electric field lines with a dielectric in place. Since some of the field lines end on charges in the dielectric (because the polarity of the dielectric is opposite that of the plates), the overall field between the plates is weaker than if there were a vacuum between the plates, even though the same charge is on the plates.
The voltage between the plates is V=Ed, so it is also reduced by the dielectric. This means there is a smaller V for the same charge Q and since C = Q/V, the capacitance is greater.
Capacitors have their own special equations for determining equivalent resistance in series or parallel, just like resistors.
For a parallel circuit, individual capacitors act as one large capacitor storing a large charge (Qtotal = Q1 + Q2 +Q3) resulting in a total capacitance that is simply the sum of the individual values.
A series circuit is a bit trickier since the charge is split up along each of the capacitors, but we can derive an expression for this by using the KVL (sum of voltage drops needs to be equal to the battery voltage)
In a DC circuit, an initially uncharged capacitor will begin storing charge on its plates, increasing its potential difference until the voltage of the capacitor is equal to the voltage of the battery or other supply source. At this point, there is no current passing through the capacitor and it acts as an open switch or a break in the wire.
For example, in the circuit below, the current initially flows through both branches, but as the voltage of C1 approaches the battery voltage, less and less current passes through R1. When steady state is reached, the circuit will appear to be a series circuit with only R2 in it.
The RC circuit is a very common type of capacitor where a resistor and capacitor are connected in series with each other. A switch is used to allow the capacitor to charge (position a) or discharge (position b).
An RC circuit is a type of electrical circuit that contains a resistor and a capacitor connected in series or parallel. RC circuits are used to filter signals, smooth out voltage fluctuations, and discharge stored energy.
Here are some key points about RC circuits:
The cool thing about RC circuits is that the charging and discharging time can be tweaked by changing the values of C and R.
Knowing the exact equations or graphs of RC Circuit equations in not on the exam but will help enhance your understanding. Graphing these functions shows us the changes in V and I as the capacitor charges. Notice how when the steady-state is reached, the current in the capacitor is basically zero.
Now we can make the same sort of graphs as we did for the charging segment.
Area charge density (σ)
: Area charge density refers to how much charge is distributed over a given area. It quantifies how concentrated or spread out charges are on a surface.Capacitance
: Capacitance is the ability of a capacitor to store electrical energy in an electric field. It is defined as the ratio of stored charge on each plate to the potential difference across them.Capacitor
: A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by a dielectric material.Dielectric
: A dielectric is an insulating material that can be placed between the plates of a capacitor to increase its capacitance. It reduces the electric field and stores electrical energy.Direct Current (DC)
: Direct current refers to the flow of electric charge in one direction only. It has constant magnitude and does not change with time.Electric field
: An electric field refers to an invisible area surrounding an electrically charged object or particle, where other charged objects experience either attraction or repulsion forces.Electric potential difference
: Electric potential difference refers to the difference in electric potential energy per unit charge between two points in an electric field. It represents the work done per unit charge to move a positive test charge from one point to another.Electrical potential energy
: Electrical potential energy is the stored energy that results from the position or configuration of charged particles within an electric field.Energy stored in a capacitor (U)
: The energy stored in a capacitor is the amount of electrical potential energy that can be stored when charges are separated by an electric field within the capacitor.Farads (F)
: Farads are units used to measure capacitance. One farad represents one coulomb of charge stored per volt applied across a capacitor.Kirchhoff's Voltage Law (KVL)
: Kirchhoff's Voltage Law states that in any closed loop or mesh within an electrical network, the algebraic sum of all voltages must be zero.Open switch
: An open switch refers to a break or interruption in an electrical circuit that prevents the flow of current.Parallel circuit
: A parallel circuit is a circuit where the components are connected side by side, providing separate paths for current flow.Parallel-plate capacitor
: A parallel-plate capacitor is a type of capacitor consisting of two flat conducting plates separated by a small distance. It has high capacitance due to its large surface area and small separation distance.Permittivity of free space (ϵ0)
: The permittivity of free space is a physical constant that represents the ability of empty space to permit the formation of an electric field. It quantifies how easily electric fields can be established in a vacuum.RC Circuit
: An RC circuit consists of both resistors (R) and capacitors (C) connected together in series or parallel. It exhibits time-dependent behavior due to charging and discharging processes within the capacitor.Resistor
: A resistor is an electrical component that restricts the flow of electric current in a circuit. It converts electrical energy into heat.Series circuit
: A series circuit is a circuit where the components are connected in a single path, so the current flows through each component one after another.9 min read•january 8, 2023
Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
A capacitor is a device that can be used to store charge, and therefore, electrical potential energy. They are used in a wide range of electrical devices including the flash on your cell phone camera. There are several different ways to construct a capacitor, but we're going to focus on the parallel-plate version.
A capacitor is a device that stores electric charge and energy in an electric field. It consists of two conductors, called plates, separated by an insulating material called the dielectric.
Here are some key points about capacitors:
The parallel plate capacitor is created by taking two conductive plates and separating them by a small distance. A dielectric is often added to increase the amount of charge a capacitor can store. We'll discuss more about dielectrics in the next section.
Let's create a simple capacitor using two metal plates and connect them to a battery to charge them up. Recall from Unit 1, that the strength of the electric field is proportional to the amount charge. E=kQ/r^2
We also know that the potential difference (V) between the plates is related to the electric field through ΔV=Ed. Following this thought process, we can see that V∝Q as well. The more charge that gets stored on each plate, the stronger the field, and the higher the voltage between the plates will be. We'll define a new quantity, capacitance(C), as the constant of proportionality between V and Q such that:
The unit for capacitance is the Farad (F), where 1F =1C/1V
Let's derive what capacitance actually is. This derivation is beyond the course but will give you a deeper understanding of circuits.
We can also define capacitance in terms of the physical dimensions of the capacitor. Recall that σ=Q/A (area charge density) for a sheet of charge, and E=σ/ϵ0 for a conductive plate.
From here, we can see that capacitance is directly proportional to the area of the plates (A) and inversely proportional to the distance between them. This should make sense since a larger plate has more room for the charge to occupy and, therefore, more should be able to fit on it.
Because the capacitor stores charge, it also stores electric potential energy (UC). The amount of energy stored can be determined through a derivation. However, the derivation requires understanding of integral calculus we will just work with the final product.
Energy in a capacitor is the energy stored in the electric field between the capacitor plates. It is a measure of the potential energy of the electric charges stored on the capacitor plates.
Here are some key points about energy in a capacitor:
Take a few minutes and check out this Phet Simulation where you can alter the physical properties of a parallel plate capacitor and see the effect on voltage, field strength, and energy stored.
1. A 20 µF parallel-plate capacitor is fully charged to 20 V. The energy stored in the capacitor is most nearly __________.
2. A capacitor with circular parallel plates of radius R that are separated by a distance d has a capacitance of C. What would the capacitance (in terms of C ) be if the plates had radius 2R and were separated by a distance d/2 ?
The capacitance depends on the area of the plate, which for a circular plate is 2πr^2
Dielectrics are insulating materials that are often used in capacitors to increase their capacitance. They help solve the problem of how to get more charge into a capacitor without having the voltage decrease. C=Aϵo/d. Modifying the equation to include a dielectric involves adding a new term κ, which is the dielectric constant. In general, the easier a material is to polarize, the higher it's dielectric constant is. Values for common dielectrics are shown below:
Material | Dielectric Constant |
Vacuum | 1 |
Air | 1.00059 |
Bakelite | 4.9 |
Fused Quartz | 3.78 |
Neoprene Rubber | 6.7 |
Nylon | 3.4 |
Paper | 3.7 |
Polystyrene | 2.56 |
Pyrex Glass | 5.6 |
Silicon Oil | 2.5 |
Strontium Titanate | 233 |
Teflon | 2.1 |
Water | 80 |
Great question! It's because a dielectric becomes polarized easily. In fact, the easier the dielectric becomes polarized, the greater its κ becomes. Let's look at an image to understand why the polarization helps increase the capacitance.
In image (a), we can see that the molecules of the dielectric become polarized and align opposing the charge on the plates. This produces a layer of opposite charge on the surface of the dielectric that attracts more charge onto the plate, because of Coulomb's Law, increasing its capacitance.
Another way to understand how a dielectric increases capacitance is to look at how it changes the electric field inside the capacitor. Image (b) shows the electric field lines with a dielectric in place. Since some of the field lines end on charges in the dielectric (because the polarity of the dielectric is opposite that of the plates), the overall field between the plates is weaker than if there were a vacuum between the plates, even though the same charge is on the plates.
The voltage between the plates is V=Ed, so it is also reduced by the dielectric. This means there is a smaller V for the same charge Q and since C = Q/V, the capacitance is greater.
Capacitors have their own special equations for determining equivalent resistance in series or parallel, just like resistors.
For a parallel circuit, individual capacitors act as one large capacitor storing a large charge (Qtotal = Q1 + Q2 +Q3) resulting in a total capacitance that is simply the sum of the individual values.
A series circuit is a bit trickier since the charge is split up along each of the capacitors, but we can derive an expression for this by using the KVL (sum of voltage drops needs to be equal to the battery voltage)
In a DC circuit, an initially uncharged capacitor will begin storing charge on its plates, increasing its potential difference until the voltage of the capacitor is equal to the voltage of the battery or other supply source. At this point, there is no current passing through the capacitor and it acts as an open switch or a break in the wire.
For example, in the circuit below, the current initially flows through both branches, but as the voltage of C1 approaches the battery voltage, less and less current passes through R1. When steady state is reached, the circuit will appear to be a series circuit with only R2 in it.
The RC circuit is a very common type of capacitor where a resistor and capacitor are connected in series with each other. A switch is used to allow the capacitor to charge (position a) or discharge (position b).
An RC circuit is a type of electrical circuit that contains a resistor and a capacitor connected in series or parallel. RC circuits are used to filter signals, smooth out voltage fluctuations, and discharge stored energy.
Here are some key points about RC circuits:
The cool thing about RC circuits is that the charging and discharging time can be tweaked by changing the values of C and R.
Knowing the exact equations or graphs of RC Circuit equations in not on the exam but will help enhance your understanding. Graphing these functions shows us the changes in V and I as the capacitor charges. Notice how when the steady-state is reached, the current in the capacitor is basically zero.
Now we can make the same sort of graphs as we did for the charging segment.
Area charge density (σ)
: Area charge density refers to how much charge is distributed over a given area. It quantifies how concentrated or spread out charges are on a surface.Capacitance
: Capacitance is the ability of a capacitor to store electrical energy in an electric field. It is defined as the ratio of stored charge on each plate to the potential difference across them.Capacitor
: A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by a dielectric material.Dielectric
: A dielectric is an insulating material that can be placed between the plates of a capacitor to increase its capacitance. It reduces the electric field and stores electrical energy.Direct Current (DC)
: Direct current refers to the flow of electric charge in one direction only. It has constant magnitude and does not change with time.Electric field
: An electric field refers to an invisible area surrounding an electrically charged object or particle, where other charged objects experience either attraction or repulsion forces.Electric potential difference
: Electric potential difference refers to the difference in electric potential energy per unit charge between two points in an electric field. It represents the work done per unit charge to move a positive test charge from one point to another.Electrical potential energy
: Electrical potential energy is the stored energy that results from the position or configuration of charged particles within an electric field.Energy stored in a capacitor (U)
: The energy stored in a capacitor is the amount of electrical potential energy that can be stored when charges are separated by an electric field within the capacitor.Farads (F)
: Farads are units used to measure capacitance. One farad represents one coulomb of charge stored per volt applied across a capacitor.Kirchhoff's Voltage Law (KVL)
: Kirchhoff's Voltage Law states that in any closed loop or mesh within an electrical network, the algebraic sum of all voltages must be zero.Open switch
: An open switch refers to a break or interruption in an electrical circuit that prevents the flow of current.Parallel circuit
: A parallel circuit is a circuit where the components are connected side by side, providing separate paths for current flow.Parallel-plate capacitor
: A parallel-plate capacitor is a type of capacitor consisting of two flat conducting plates separated by a small distance. It has high capacitance due to its large surface area and small separation distance.Permittivity of free space (ϵ0)
: The permittivity of free space is a physical constant that represents the ability of empty space to permit the formation of an electric field. It quantifies how easily electric fields can be established in a vacuum.RC Circuit
: An RC circuit consists of both resistors (R) and capacitors (C) connected together in series or parallel. It exhibits time-dependent behavior due to charging and discharging processes within the capacitor.Resistor
: A resistor is an electrical component that restricts the flow of electric current in a circuit. It converts electrical energy into heat.Series circuit
: A series circuit is a circuit where the components are connected in a single path, so the current flows through each component one after another.© 2024 Fiveable Inc. All rights reserved.
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