Capacitor charging time. Relative dielectric constant. Capacitor device. What does capacity depend on?

But there are other components that serve to accumulate electrical energy, namely the capacitor that we will introduce today and the inductor that we will introduce later. These two components form a group called "reagents", and when they are ideal, that is, they have no losses, which can be considered resistive components, never heat up. They accumulate and exchange energy between them.

Remember when we charge a metal body with positive and negative charges? And then we connect them to a metal rod. The organs were discharged by circulating electrons from the negative to the positive body until both were in the same electric potential. Internal structure The capacitor reminds us of this experience. In fig. 1 you can see two metal balls forming an elemental capacitor.

With the help of this simple device we're going to establish some very precise concepts. To charge our device, we can keep its top bar on the positive end of the battery and its terminal below the negative one. Immediately, electrons circulate from the stack to the lower ball and from the upper ball to the stack.

This circulation is only instantaneous when the bars are maintained; after some time the circulation stops because a balance of charges has occurred. If we could measure the voltage between two rods using an infinite meter internal resistance, we would notice that the metal balls have a potential difference, equal to voltage cells.

The most interesting thing is that the voltage at which the elementary capacitor was charged is never lost even after disconnecting the device from the battery. If the formed capacitor is perfect and the meter has infinite resistance, it can measure the same voltage every other hour.

As you know from our specialty, everyone has a representation through a diagram. In Figure 2 we can observe a representation of our elementary capacitor with a very characteristic shape forming a circuit that will allow us to charge and discharge the capacitor. The element that converts the charge circuit into a discharge circuit is called an inverter switch and has a metal foil that is in physical contact with one or another section of the circuit.

This is a difficult circuit for a beginner; so let's explain it in detail. These blades rotate on the two terminals on the left and alternately connect the top or bottom terminals on the right. Luis Davila with the title "Using a Multimeter". In fact, an oscilloscope allows you to watch how the voltage changes across a capacitor over time. We can say that it is a density plotter, equivalent to measuring with a counter every second and plotting the result.

Explaining a procedure in words is extremely tedious, so we use a procedure summarized in symbolic form. Finally, left-click on the battery transfer and drop down to the desktop where you want to find the battery. Then go to the diagram as indicated in the previous lesson.

After assembling the circuit or at the moment of gluing each component, you need to assign it a value. Double click on the selected component and a dialog box will appear as shown in the figure. In the same way, we double click on the capacitor and the dialog box in Figure 5 will appear with the power units. To do this, select the icon with the colored stripes and then open the graphic below the outline. When you click on the image, a screen appears that allows you to select scales.

Predisposing him to the next drawing. The desired plot can be seen in Figure 7. In fact, the capacitor does not discharge, ever remaining charged with a value that drops 38.4% from the value having 1 µS before. This type of curve is called exponential and always occurs when a reactive component combines with a resistive component. In our charge and discharge circuit, we use a double switch to disconnect the two terminals of our capacitor.

Capacitor Charge Curve

In fact, both the negative terminal of the battery and the lower terminal of the resistor and the lower terminal of the capacitor can be permanently connected to ground, as this is enough to interrupt at one point in the circuit to stop the current. Just as a capacitor discharges exponentially, it also charges exponentially when there is a resistor between the battery and the capacitor known value. In fig. 10, a circuit can be observed in which the capacitor is charged from a 10V source or discharged to ground when the switch is moved.

When the switch is raised the capacitor is charged and the voltage rises, when it falls the resistor is connected and the voltage is low. Here we need to explain two very important things about simulation. You can actually select the key you want because by double-clicking the key, a dialog box will appear that will ask you which key you want to control. Secondly, it is impossible to open and close a key in two millionths of a second. Of course we take seconds between pressed and pressed.

It happens that the simulation does not run in real time. In fact, the circuit is not actually assembled, but solves equations, but at such a speed that they can be represented on a graph; although not in real time. The simulated time can be read at the bottom of the screen where it says "time". Can you easily explain why the voltage changes exponentially as a capacitor discharges? You must use mathematics to prove this, but it is preferable to anticipate the motive before performing a purely academic demonstration.

Analyzing our example, we can say that when a capacitor is charged at 10V and a 1 ohm resistor is connected across it, the current flowing through the resistor is 10A and therefore the voltage drop across the resistor is equal to the source voltage. When a capacitor discharges across a resistor, the voltage is less and therefore each time it draws less current, and then it makes sense that the capacitor takes longer to discharge. For example, when a microsecond passed a voltage of 3.8 V and only a resistance of 3.8 A by a resistor.

Is it possible to charge a capacitor linearly? Sure, but it must be charged by a constant current source, not a constant voltage source like a battery. What is a constant current source? A constant voltage source is a voltage whose output voltage does not change with the load current. Instead the source direct current is any source that provides a constant output current regardless of load resistance. For example, a 1A DC source will deliver this current either into a 1 ohm charge or into a 10 ohm load.

Note that when charging a capacitor at constant current, the exponential curve converts to a straight line, resulting in many useful schemes, which we gradually learn. The same result can be obtained using the DC source symbol. In fact, if you want, you can consider DC supplies to be just an electronic abstraction, since they don't exist as a real component. As shown in FIG. 11, circuit change can work with constant current source.

Because the student can observe that the circuits generate the same signal across the capacitor and are therefore equivalent. In this lesson we met the second most important character in electronics. In fact, we are only presenting it because we have not yet explained how a real capacitor is made.

So far our capacitor is two metal balls separated by an insulator, which is air. We never specify the size of these balls needed to create a 1uF capacitor like the one we used in the explanation. This capacitor should have a diameter of about several kilometers. But fortunately, the current industry offers us solutions as small as a cylinder with a diameter of 3 mm by 3 heights.

In the next lesson we will finish the topic explaining what it is ceramic capacitor, polyester and electrolytic capacitor, and first of all, we will focus on the last one, because it is one of the components with highest level failures and for the fact that it has the peculiarity of being a polarized component.

We have flat capacitor circular radio plates separated by distance. Current flows into the capacitor. Calculate the bias current inside the capacitor. This electric field is time dependent, and the displacement current is proportional to the time derivative of the electric flux of this field. This is because the charge carrying the current cannot pass through the capacitor and is deposited on the capacitor plate.

We then assume that the electric field between the plates of the capacitor is uniform and perpendicular to the plates. The vector is a unit vector that comes from the positive to the negative plate. In paragraph 2 we saw that the field created between two plates with charge densities of the same absolute value and opposite signs, was.

Where σ is the surface charge density. The area of ​​the plates is the capacitor. Then the electric field between the plates can be written down. Let's calculate the bias current flowing through the capacitor. The electric flux through the surface parallel to the plates is.

Since the electric field is uniform, we have. Displacement current. But this value is equal to the current that reaches the plates. We then see that the bias current between the plates of the capacitor is equal to the conduction current in the cable. This fact makes the Ampere-Maxwell law applicable to any surface supported by a closed curve.

In a figure system, consider two surfaces supported on a closed curve Γ. Although, if we do two on the surface, we have. It should be noted that the fact that the conduction current in the cable and the displacement current inside the capacitor are numerically equal does not mean that we can also write the Ampere-Maxwell law.

The leading current and bias current appear in different places. Conduction in the cable and displacement inside the capacitor. Diodes can be connected in such a way that they change the sign of one of the half-cycles. Thus, instead of eliminating the half-cycle, it can be used to obtain the maximum input current output.