# CAPACITORS

Subject:

Term:

FIRST TERM

Week:

WEEK 8

Class:

SS 3

Topic:

## CAPACITORS

CONTENT

1. Definition of a Capacitor
2. Energy Stored in a Capacitor
3. Arrangement of Capacitors
4. Solved Questions

Definition of a Capacitor

A capacitor or condenser is a device that stores energy in the electric field between two closely spaced conductors (called “plates”). A capacitor can store charge by holding a difference of potential across its plates. A metal plate possesses the property of being absolute zero, which means that it has no net charge and thus gives up any stored charge when connected to another conductor. If the metal plate was only connected to a wire, then no current would flow. This is because there are no extra electrons to be transferred, and the absolute zero state of the junction point remains constant.

What happens when we connect two plates together? The charges that were previously held on one plate will move over to neutralize the other plate. The process of moving an existing charge from one plate to another is called “charging”.

When we charge a capacitor, we transfer electrons in order to create a surplus of negative charges on one plate, and an equal number of positive charges on the other plate. Once this process is complete, both plates will have identical amounts of charge, and the voltage across the plates will be zero.

Since capacitors are capable of storing charge between two conducting surfaces, it is easy to see how this property can be used in a number of different applications. By placing a capacitor in a circuit where there is an alternating current (AC), we can make use of the large amount of energy storage in order to filter the AC and smooth out any spikes.

Capacitors can also be used to store transient energy from a battery, which is often needed for startup or when power sources are otherwise unavailable. This property allows capacitors to act as both buffer and filter elements in circuits where constant power must be supplied to some electrically powered device.

Capacitors are also used in a variety of electronic systems, such as power supplies, audio amplifiers, and radio transmitters. In these applications, the capacitor’s ability to store charge can be used to moderate an electrical signal that varies with time. As a side effect of this property, capacitors will tend to dampen any oscillations in a circuit, thereby stabilizing the signal.

A capacitor is an extremely versatile and useful electrical component, with a wide range of applications. Whether you are building an electronic circuit or working with AC power systems, there is sure to be a need for at least one capacitor in your designs!

### What is meant by a dielectric substance?

A dielectric substance is a material that can be used as the dielectric layer in a capacitor. This type of material has special properties that allow it to store and regulate electrical charge, while maintaining a constant voltage across the conductive plates of the capacitor. Some common examples of dielectric substances include ceramic materials, plastics, air, and certain types of fluid. The physical and chemical properties of these materials determine how well they can be used in various capacitive applications, as well as their overall performance characteristics. For example, some dielectric substances may have a high breakdown voltage, which means that they can store more charge for a given surface area. Other dielectric materials may have a low dielectric constant, which means that they can maintain a consistent voltage even when the surface area of the capacitor is reduced. Additionally, some materials may be more stable over time, or better suited for specific temperature ranges, depending on their chemical composition.

## List five factors which determine the capacitance of a parallel plate capacitor.

1. The thickness of the dielectric layer between the conductive plates of the capacitor.
2. The area of each conductive plate, relative to the total surface area of both plates combined.
3. 3The distance or “spacing” between the two conductive plates, which determines how much charge can build up between them.
4. The permittivity, or ability of the dielectric material to regulate electrical charge.
5. The physical characteristics and conductivity of the conductive plates themselves, including their shape, surface area, and overall geometry.

### State four effects each of them has on the capacitance.

1. The effect of a thicker dielectric layer on the capacitance would be to increase it, as this will allow for more charge to accumulate between the conductive plates.

2.An increase in the area of each conductive plate will also result in an increase in capacitance, since there will be more surface area available for storing charge.

3.A decrease in the spacing between the plates will result in an increase in capacitance, as this will allow more charge to accumulate between them.

4.The effect of a higher permittivity dielectric on the capacitance would be to increase it, since this will allow for more charge to accumulate between the conductive plates.

Other factors, such as the plate geometry and material composition, may also be affected by a change in permittivity. Additionally, some dielectric materials may have different permittivity values depending on temperature or other conditions. Therefore, it is important to carefully consider all of these factors when designing a parallel plate capacitor with specific capacitance requirements.

Energy Stored in a Capacitor.

A capacitor is a device that can store electrical energy in the form of an electric field. When two conductive plates are separated by a dielectric substance, and a voltage is applied across them, there will be an accumulation of charge between the plates due to the principle of electrostatics. The total amount of stored energy in this arrangement is directly proportional to the amount of charge that can accumulate between the plates, as well as the capacitance value of the capacitor. This stored energy can then be released or used in a variety of applications, ranging from simple electrical circuits to complex electronic devices.

## Arrangement of Capacitors

Capacitors can be arranged in a circuit in parallel or in series.

Series Arrangement

Here, the capacitors are connected end to end as shown below. For capacitors in series;

(i) Equal charge Q will be stored in the capacitor.

Q1=Q2=Q3

(ii) The sum of the potential difference across each plate is equal to the potential difference supplied by the source.

V=V1+V2+V3

but,

C=QV

Hence,  V=QC

Substituting this into the expression for V,

QC=QC1+QC2+QC3

Cancelling Q out,

1C=1C1+1C2+1C3 ——–(iv)

The reciprocal of the equivalent capacitance for capacitor in series is equal to the sum of the reciprocal of the individual capacitors in the series.

### Parallel Arrangement

Here, capacitors are arranged as shown below. For capacitor in parallel,

(i) The potential difference across the plates of the capacitor is equal.

V=V1=V2=V3

(ii) The total charge stored is the sum of all the charged stored in each capacitor.

Q=Q1+Q2+Q3

but,

C=QV

Hence,  Q=CV

substituting this into the expression for Q,

CV=C1V+C2V+C3VC=C1+C2+C3——–(v)

The equivalent capacitance for capacitors in parallel is the sum of capacitance for the individual capacitor.

Solved Questions

1. A work of 30 J is done to transfer 5 mC of charge from a point B to a point A in an electric The potential between B and A is

Solution:

Charge Q = 5 mC

Work = 30J

Note that W = QV

V=WQ=305×10−3=6000V

2. A capacitor of capacitance 3.0µF is subjected to a 2000 V potential difference across its Calculate the energy stored in the capacitor

Solution:

Capacitance C = 3.0µF

Potential difference V = 2000V

Energy E =?

Recall that E=12CV2E=3.0×10−6×600022E=54J

3. A series arrangement of three capacitors of value 8µF, 12µF and 24µF is connected in series with a 90V battery.

(i) Draw an open circuit diagram for this arrangement

(ii) Calculate the effective capacitance in the circuit

(iii) On close circuit, calculate the charge on each capacitor when fully charged

(iv) Determine the voltage across the 8µF

Solution:

1. 2. For capacitors in series, effective capacitance is given as:

1C=1C1+1C2+1C31C=18+112+124=3+2+1241C=624

Taking the reciprocal of both sides,

C1=246

Effective capacitance C=4µF

3. Recall for capacitors in series,

The charge stored on each capacitor is equal

Q=CVQ=4µ×90Q=4×10−6×90Q=3.6×10−4C

4. Recall, Q=CVV=QCV=3.6×10−48×10−6V=0.45×102=45V

The voltage across the 8µF capacitor is 45V

EVALUATION

1. The plate of a parallel plate capacitor, 5.0 x 10-3m apart are maintained at a potential difference of 5.0 x 104 calculate the magnitude of the:

• electric field intensity between the plate
• force on the electron
• acceleration of the electron

(Electronic charge = -1.6 x 10-19C, mass of electron = 9.1 x 10-31kg)

2. A capacitor of capacitance 3.0µF is subjected to a 200V potential difference. Calculate the energy stored in the capacitor