Chapter 10

Capacitors and Capacitance

Capacitance

Capacitor

Stores charge

Two conductive plates separated by insulator

Insulating material called dielectric

Conductive plates can become charged with opposite charges

Definition of Capacitance

Amount of charge Q that a capacitor can store depends on applied voltage

Relationship between charge and voltage given by

Q = CV or C = Q/V (Similar to Ohm’s Law)

Definition of Capacitance

C is capacitance of the capacitor

Unit is the farad (F)

Capacitance of a capacitor

One farad if it stores one coulomb of charge

When the voltage across its terminals is one volt

Effect of Area

Capacitance is directly proportional to amount of charge

Larger plate will be able to hold more charge

Effect of Area

Capacitance is directly proportional to plate area

If plate area is doubled, capacitance is doubled

Effect of Spacing

As plates are moved closer together

Force of attraction between opposite charges is greater

Capacitance

Inversely proportional to distance between plates

Effect of Spacing

Double the distance between plates

Capacitance becomes half as much

Effect of Dielectric

If a dielectric other than air is used between the plates

More charge can build up on the plates

The factor by which the capacitance increases

Dielectric constant or the relative permittivity

Effect of Dielectric

Permittivity

How easy it is to establish electric flux in a material

Represented by ε (Greek letter epsilon)

Capacitance of a Parallel-Plate Capacitor

Directly proportional to plate area

Inversely proportional to plate separation

Dependent on dielectric

A farad is a very large unit

Electric Flux

Electric fields

Force fields in region surrounding charged bodies

Direction of this field is direction of force on a positive test charge

Field lines never cross

Electric Flux

Density of lines indicate field strength

Electric field lines are indicated by y (Greek letter psi)

Electric Fields

Strength of an electric field is force that field exerts on a small test charge

E = F/Q

Electric flux density = total flux/area

D = y/A

Electric Fields

Flux is due to the charge Q

The number of flux lines coming from a charge is equal to the charge itself

y = Q

Field of a Parallel-Plate Capacitor

To move a charge from the negative plate to the positive plate requires work

Work = Force × distance

Voltage = Work/charge

E = V/d

Field of a Parallel-Plate Capacitor

Electric field strength between plates

Equal to voltage between them

Divided by distance between them

Voltage Breakdown

If voltage is increased enough, dielectric breaks down

This is dielectric strength or breakdown voltage

Voltage Breakdown

Breakdown can occur in any type of apparatus where insulation is stressed

Capacitors are rated for maximum operating voltage

Nonideal Effects

Leakage current

Equivalent Series Resistance

Dielectric Absorption

Temperature Coefficient

Fixed Capacitors

Ceramic Capacitors

Values change little with temperature, voltage, or aging

Plastic Film Capacitors

Mica Capacitors

Low cost, low leakage, good stability

Fixed Capacitors

Electrolytic Capacitors

Large capacitance at low cost

Polarized

Surface Mount Capacitors

Variable Capacitors

Used to tune a radio

Stationary plates and movable plates

Combined and mounted on a shaft

A trimmer or padder capacitor is used to make fine adjustments on a circuit

Capacitors in Parallel

Total charge on capacitors is sum of all charges

Q = CV

C_TE = C₁V₁ + C₂V₂ + C₃V₃

All voltages are equal

Capacitors in Parallel

C_T = C₁ + C₂ + C₃

Total capacitance of capacitors in parallel

Sum of their capacitances (like resistors in series)

Capacitors in Series

Same charge appears on all capacitors

Total V

Sum of individual voltages (like resistors in parallel)

Capacitors in Series

Capacitor Voltage

Voltage across a capacitor does not change instantaneously

Voltage begins at zero and gradually climbs to full voltage

Capacitor Voltage

Full voltage is source voltage

May range from nanoseconds to milliseconds

Depending on the resistance and capacitance

Capacitor Current

During charging

Electrons move from one plate to another

Current lasts only until capacitor is charged

Capacitor Current

Current

Large initial spike to zero

No current passes through dielectric

Energy Stored in a Capacitor

A capacitor does not dissipate power

When power is transferred to a capacitor

Stored as energy

Capacitor Failures and Troubleshooting

Reasons for capacitor’s failure

Excessive voltage, current, or temperature, or aging

Test with an ohmmeter

Good capacitor will read low, then gradually increase to infinity

Capacitor Failures and Troubleshooting

Capacitor short

Meter resistance will stay low

Capacitor Failures and Troubleshooting

If capacitor is leaky

Reading will be lower than normal

If open

Stays at infinity


	Capacitor
		Stores charge
		Two conductive plates separated by insulator
		Insulating material called dielectric
		Conductive plates can become charged with opposite charges


	Amount of charge Q that a capacitor can store depends on applied voltage
	Relationship between charge and voltage given by
	Q = CV or C = Q/V (Similar to Ohm’s Law)


	C is capacitance of the capacitor
	Unit is the farad (F)
	Capacitance of a capacitor
		One farad if it stores one coulomb of charge
		When the voltage across its terminals is one volt


	Capacitance is directly proportional to amount of charge
	Larger plate will be able to hold more charge


	Capacitance is directly proportional to plate area
	If plate area is doubled, capacitance is doubled


	As plates are moved closer together
		Force of attraction between opposite charges is greater
	Capacitance
		Inversely proportional to distance between plates


	Double the distance between plates
		Capacitance becomes half as much


	If a dielectric other than air is used between the plates
		More charge can build up on the plates
	The factor by which the capacitance increases
		Dielectric constant or the relative permittivity


	Permittivity
		How easy it is to establish electric flux in a material
		Represented by ε (Greek letter epsilon)


	Directly proportional to plate area
	Inversely proportional to plate separation
	Dependent on dielectric


	A farad is a very large unit


	Electric fields
		Force fields in region surrounding charged bodies
	Direction of this field is direction of force on a positive test charge
	Field lines never cross


	Density of lines indicate field strength
	Electric field lines are indicated by y (Greek letter psi)


	Strength of an electric field is force that field exerts on a small test charge
		E = F/Q
	Electric flux density = total flux/area
		D = y/A


	Flux is due to the charge Q
	The number of flux lines coming from a charge is equal to the charge itself
		y = Q


	To move a charge from the negative plate to the positive plate requires work
	Work = Force × distance
	Voltage = Work/charge
	E = V/d


	Electric field strength between plates
		Equal to voltage between them
		Divided by distance between them


	If voltage is increased enough, dielectric breaks down
	This is dielectric strength or breakdown voltage


	Breakdown can occur in any type of apparatus where insulation is stressed
	Capacitors are rated for maximum operating voltage


	Leakage current
	Equivalent Series Resistance
	Dielectric Absorption
	Temperature Coefficient


	Ceramic Capacitors
		Values change little with temperature, voltage, or aging
	Plastic Film Capacitors
	Mica Capacitors
		Low cost, low leakage, good stability


	Electrolytic Capacitors
		Large capacitance at low cost
		Polarized
	Surface Mount Capacitors


	Used to tune a radio
	Stationary plates and movable plates
		Combined and mounted on a shaft
	A trimmer or padder capacitor is used to make fine adjustments on a circuit


	Total charge on capacitors is sum of all charges
	Q = CV
	C_TE = C₁V₁ + C₂V₂ + C₃V₃
	All voltages are equal


	C_T = C₁ + C₂ + C₃
	Total capacitance of capacitors in parallel
		Sum of their capacitances (like resistors in series)


	Same charge appears on all capacitors
	Total V
		Sum of individual voltages (like resistors in parallel)


	Voltage across a capacitor does not change instantaneously
	Voltage begins at zero and gradually climbs to full voltage


	Full voltage is source voltage
	May range from nanoseconds to milliseconds
		Depending on the resistance and capacitance


	During charging
		Electrons move from one plate to another
	Current lasts only until capacitor is charged


	Current
		Large initial spike to zero
	No current passes through dielectric


	A capacitor does not dissipate power
	When power is transferred to a capacitor
		Stored as energy