Capacitance
Source: Yong P. Chen, PhD, Department of Physics & Astronomy, College of Science, Purdue University, West Lafayette, IN
This experiment will use comme…
1. Charging a Capacitor
- Obtain a commercial capacitor with capacitance C = 470 µF (or some similar value), a programmable voltage source, and an amp-meter (or multi-meter that can measure current).
- With the voltage source set to 0 V, connect the "+" terminal of the voltage source to one terminal of the capacitor, with the amp-meter in between, and connect the "−" terminal of the voltage source to the other terminal, as in Figure 1. The connection can be made with cables with clamps or banana plugs into receiving ports on the capacitor and instruments.
- Switch the voltage source from 0 V to 1 V (in about 1 s), and observe the transient current reading on the amp-meter. Do the same for 2 V, 5 V, and 10 V (for each target voltage; this means first go back to 0 V, then switch to the target voltage in about 1 s). Note that the transient current is larger for a larger target voltage, as expected from Equation 2.
- Program the voltage source to generate a voltage ramp from 0 V to 10 V in 5 s, and record the "steady state" reading of the amp-meter during the middle of the ramp. Repeat for a ramp time of 10 s, 20 s, and 30 s. Plot the observed current versus the voltage ramp rate (in V/s).
2. Tuning the Capacitance
- Turn off the voltage source and replace it with a 300 V battery, and replace the amp-meter by a 1 MΩ resistor (the purpose of this resistor is to provide extra protection to limit the current in the circuit); also replace the commercial capacitor with a parallel plate capacitor with an adjustable separation between the plates.
- Obtain a high-impedance voltmeter (or "electrometer") and connect it to measure the voltage difference V between the two plates (the high impedance impedes the discharge of the capacitor during the experiment when the electrometer is connected). See Figure 5.
- Connect the 300 V battery to the parallel plate capacitor, wait until the electrometer reaches the steady state of 300 V (now the capacitor is fully charged by the 300 V source), and then quickly disconnect the voltage source from the plates. See Figure 6. The electrometer should still read 300 V.
- Now increase the distance d between the plates to larger values such as 15 mm, 10 mm, and 5 mm, and observe and record the corresponding voltage reading on the electrometer (V); plot V versus d.
- Increase d back to ~ 20 mm, insert a plastic slab between the two plates and observe what happens to V read by the electrometer. The reduction of V between the plates (with charge Q fixed in this case) results from the larger dielectric constant ε of the plastic (compared to air) as the medium of the capacitor (refer to Equations 1 and 3).
3. Parallel and Series Capacitances
- Obtain a capacitance meter (a "LCR meter" or a multi-meter with a capacitance measurement mode); obtain a breadboard to facilitate the electrical connections in this part of the experiment.
- Obtain two commercial "ceramic" capacitors with a capacitance of 1 µF, and use the capacitance meter to verify their capacitance, as in Figure 2.
- Connect the two capacitors in parallel, and use the capacitance meter to measure the total capacitance (between points A and B, see Figure 3).
- Connect the two capacitors in series, and use the capacitance meter to measure the total capacitance (between points A and B, see Figure 4).
Figure 3: Diagram showing two capacitors connected in parallel.
Figure 4: Diagram showing two capacitors connected in series.
Figure 5: Diagram showing the charging up of a capacitor using a voltage source, while reading the voltage with an electrometer.
Figure 6: After quickly disconnecting the voltage source in Figure 5, the voltage and charge on the capacitor should remain.
A capacitor is essential in circuits because it resists changes in voltage by storing equal and opposite charges on its conductive terminals and then supplying energy when the voltage supply drops.
A capacitor is composed of two conductive terminals, such as the two plates in a "parallel plate capacitor", separated by an insulating material or gap. When voltage is applied across a capacitor, it draws current. This causes electrons to accumulate on one plate while they are repelled on the other, thus storing equal and opposite charges on the two plates.
The ability of the component to store charge is called capacitance, and is measured in units called Farads.
This video uses a parallel plate capacitor to illustrate the concept of capacitance and its dependence on physical factors and network configuration.
When a power source is applied to a circuit, the capacitor draws "charging current" until its conductors are fully charged. The amount of charge 'Q' a capacitor can store depends on the capacitance 'C' of the component, and the magnitude of the supplied voltage 'V'.
When the voltage drops, charge from the capacitor's conductors flows to the circuit, generating current until the stored charge is depleted, thus stabilizing voltage fluctuation. Current is the rate of change in the amount of charge. Combining this with the previous equation, we can say that the current flow out of the capacitor is capacitance times the rate of change in voltage.
The value of C is constant for a given capacitor, and can be obtained by using this equation, which shows that C is directly proportional to A -- the plate surface area, d -- the gap distance, and epsilon -- the dielectric constant or "permittivity" of the insulating material between the plates.
Dielectric constant is a measure of the extent to which the material becomes polarized in an electric field.
Thus, given the relationship between epsilon and C, and C and Q; at a given voltage, higher the permittivity, higher will be the capacitor's charge storage capacity.
Vacuum has a dielectric constant of 8.85x10-12 Farads per meter, denoted ?0. Other media generally have greater permittivity values, which are scaled to ?0 and termed the "relative" permittivity of the medium. For example, the relative permittivity of air is approximately one, polymers range from 2 to 4, and distilled water is 80.
Now that physical properties effecting capacitance have been explained, let's take a look at how to measure capacitance in individual or networked capacitive elements.
To start, gather the following materials: a commercial capacitor with capacitance close to 470 micro farad, a programmable voltage source, and an amp-meter or multi-meter that can measure current.
Next, with the voltage source set to 0 V, connect its positive terminal to the amp-meter. Then connect the other port of the amp-meter to the capacitor, using cables with clamps or banana plugs. This enables the measurement of output current from the capacitor. Following that connect the negative port of the voltage source to the other terminal of the capacitor.
Then, switch the voltage source from 0 to 1 V and observe the transient current reading on the amp-meter. Next adjust the voltage back to 0 before increasing to 2 V, 5 V and finally 10 V. For each target voltage allow one second of rest at 0 V between changes to different target voltages. Observe the transient current as the voltage changes.
As predicted by the equation the transient current is expected to be larger for a larger target voltage.
Lastly, program the voltage source to generate a voltage ramp from 0 V to 10V over 5 seconds, and record the "steady state" amp-meter reading mid-ramp. Next, repeat for ramp times of 10 s, 20 s, and 30 s.
Now obtain a parallel plate capacitor with adjustable separation between the plates, and use a 300V battery as the voltage source. Replace the amp-meter with a 1 mega-ohm resistor. This resistor provides an extra protection limiting the current flow in the circuit.
Second, connect a high-impedance voltmeter, or electrometer, between the two plates in order to measure the voltage difference.
Next, connect the battery to the capacitor, and wait until the electrometer also reaches the steady state of 300 V, indicating the capacitor is fully charged. Then quickly disconnect the battery from the plates. The electrometer should still read 300 V.
Repeat the measurement after decreasing the distance between the plates to 15, 10, and 5 mm.
Finally, with a capacitor plate distance of 20 mm, insert a plastic slab between the two plates and observe what happens to the electrometer voltage reading.
For the commercial capacitor, the plot of measured current versus voltage ramp rate reveals a linear relationship between the two parameters.
This complies with the relationship predicated by this equation, which we derived earlier in the video. As per the equation, the slope of the line is equal to the capacitance.
For the parallel plate capacitor with fixed charge, the plot of voltage between the plates versus distance between the plates is linear. This again supports the theoretical relationships. We know that capacitance and plate distance are inversely proportional. We also know that when conductor charge is fixed, capacitance and voltage are also inversely proportional. Combining these two equations reveals that voltage and plate distance are directly proportional to each other when the charge is fixed.
This equation also predicts that with a fixed charge, the larger dielectric constant of the gap medium, the lower would be the voltage between the plates. This was confirmed when the air in the gap was replaced by plastic and we saw a drop in the voltmeter reading.
Capacitors are used in a large variety of engineering and scientific applications to store charge and selectively discharge electricity.
Capacitors are essential for electrical signal processing. For example, biologists used a two-choice test to evaluate how mice recognize and respond to different ultrasonic vocalizations. First, sound files are recorded from live mice and trimmed using high pass filters to select for frequency.
High-pass filter circuits use capacitors to block low frequency oscillations, as the conduction between capacitor plates generally increases at higher frequencies and decreases at low frequencies. Then, variable frequency sounds are simultaneously played in two separate locations, allowing mice to migrate towards the preferred vocalization.
While mains supplies are AC with fluctuating current, many electronic devices, such as computers, require DC power. Capacitors are used within AC power adapters to filter electrical signals and stabilize the DC supply, providing a smooth, uninterrupted source.
You've just watched JoVE's introduction to capacitors. You should now understand the concept of capacitance, how to measure this physical parameter, and how properties like plate-to-plate distance or gap material effect the capacitance value. As always, thanks for watching!
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Q1: What is capacitance and how does a capacitor store charge?
Capacitance is the ability of a capacitor to store charge, measured in Farads. A capacitor consists of two conductive plates separated by an insulating material. When voltage is applied, electrons accumulate on one plate while being repelled from the other, creating equal and opposite charges. This charge storage stabilizes voltage fluctuations in circuits.
Q2: How does plate separation affect capacitance in a parallel plate capacitor?
Capacitance is inversely proportional to the distance between plates. As the gap distance decreases, capacitance increases, allowing the capacitor to store more charge at the same voltage. This relationship is described by the equation C = εA/d, where d is the plate separation, A is plate area, and ε is the dielectric constant.
Q3: What role does dielectric material play in capacitor performance?
The dielectric material between capacitor plates determines the permittivity, or dielectric constant, which directly affects charge storage capacity. Materials with higher permittivity values, such as distilled water with a relative permittivity of 80 compared to air's value of one, enable capacitors to store significantly more charge at a given voltage.
Q4: How is current related to voltage changes in a capacitor?
Current flowing through a capacitor equals capacitance multiplied by the rate of voltage change over time. When voltage changes rapidly, larger transient currents flow. This relationship explains why capacitors pass high-frequency signals while blocking low-frequency oscillations, making them useful in high-pass filter circuits for resistor capacitor resistor inductor and inductor capacitor circuits.
Q5: What happens when a capacitor discharges after the voltage supply is removed?
When voltage is disconnected, stored charge flows from the capacitor's conductors back into the circuit, generating current until the charge is depleted. This discharge process stabilizes voltage fluctuations by supplying energy when the external voltage supply drops, making capacitors essential for maintaining steady electrical signals.
Q6: How do capacitors function in AC power adapters and signal processing?
Capacitors filter electrical signals and stabilize DC supplies in AC power adapters, providing smooth, uninterrupted power to devices like computers. In signal processing, capacitors in high-pass filter circuits block low-frequency oscillations while allowing higher frequencies to pass, enabling selective frequency filtering in applications like ultrasonic vocalization analysis.
Q7: What physical factors determine the capacitance value of a parallel plate capacitor?
Capacitance depends on three physical factors: plate surface area (A), gap distance (d), and the dielectric constant (ε) of the insulating material. The relationship is C = εA/d, showing capacitance increases with larger plate area and higher permittivity, but decreases as the gap distance increases.