**Easy-to-Understand **Capacitor Models

for Physics & Engineering Students

A hydraulic capacitor is a cylinder divided by a flexible rubber sheet. Here's an oblique view and a cross-section side view.

Imagine that the stretchiness and physical proportions of the rubber sheet are designed so that the
volume of water stored is proportional to the pressure applied:

The constant of proportionality is called the capacitance, which has units of liters per kPa. In this example, the capacitance is 0.01 liter per kPa.Volume = Capacitance x Pressure

1 liters = 0.01 liters/kPa x 100 kPa

2 liters = 0.01 liters/kPa x 200 kPa

3 liters = 0.01 liters/kPa x 300 kPa

Consider the change over time:

(

Then you get:

Flow Rate = Capacitance x (dP/dt)where dP/dt means the change in pressure per unit of time.

For example, if you increase the pressure at a rate of 100 kPa per second, the flow rate into the capacitor is 1 liter per second.

1 LPS = 0.01 liter/kPa x 100 kPa/sec

When you apply a voltage across of the capacitor, charge is stored in the capacitor.

The amount of charged stored is proportional to the voltage applied:

The constant of proportionality is called the capacitance, and it has units of coulombs per volt, also known as Farads. In this example, the capacitance is 0.01 coulombs per volt, or 0.01 Farad.Charge = Capacitance x Voltage

1 coulomb = 0.01 farad x 100 volts

2 coulombs = 0.01 farad x 200 volts

3 coulombs = 0.01 farad x 300 volts

Consider the change over time:

(

Then you get:

Current = Capacitance x (dv/dt)where dv/dt means the change in voltage per unit of time.

This is the same equation you see in your physics textbook:

For example, if you increase the voltage at a rate of 100 volts per second, the flow rate into the capacitor is 1 coulomb per second (1 amp).

1 amp = 0.01 F x 100 volts/sec

Energy = 1/2 x Pressure x Volume (hydraulic)For the hydraulic capacitor, the stored energy comes from the pump that pushed the water into the capacitor. The

Energy = 1/2 x Voltage x Charge (electronic)

Similarly, for the electronic capacitor, the stored energy comes from the voltage source that pushed the charge into the capacitor. The

You can extract the energy by connecting a resistor between the two ends of the capacitor. This causes a current to flow through the resistor. The voltage and current both decay exponentially until the voltage reaches zero and all the energy is dissipated as heat in the resistor.

For example, connecting a 100 V battery to a 1 Farad capacitor draws 50 coulombs of charge into the positive side of the capacitor, leaving -50 coulombs on the negative side.

Then the capacitor has a net charge of zero (50 coulombs + -50 coulombs) but a difference of 100 coulombs on the two sides. When the battery is disconnected, the voltage difference remains because the charge is trapped in the capacitor.

The physical attraction of opposite charges holds the positive and negative charge in place. That's why a capacitor is made with closely spaces parallel plates -- to get the opposite charges as close together as possible, over as large an area as possible.

An electric field exists in the space between the two plates, which causes any charged object in that space to feel a force. For example, a free electron is attracted to the positively charged plate and repelled by the negatively charged plate.

If you short-circuit the two terminals of the capacitor, the charge rushes back from the positively charged side to the negatively charged side, bringing the charge back to zero on both sides.

A capacitor works fine with just empty space or air between the plates. However, the capacitance can be increased greatly by putting dielectric material between the plates, that is, a material whose molecules are polar (they each have a positive and a negative side), and the molecules have the ability to move or at least turn in place. Liquid water and ice are examples of dielectric materials.

The positive and negative plates attract the negative and positive ends of the molecules, respectively, so the molecules move or turn to face the opposite type of charge on each plate. This has the effect of decreasing the electric field inside the dielectric material but increasing the electric field just outside the material, facing toward the plates. Therefore, the plates see a stronger electric field, and more charge can be stored for the same applied voltage.

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