Principles & Applications Electricity Principles & Applications Sixth Edition Richard J. Fowler Chapter 10 Capacitance ©2003 Glencoe/McGraw-Hill

INTRODUCTION Capacitor Terminology Use of Capacitors Capacitors in Ac and Dc Circuits Series and Parallel Capacitors Time Constants Capacitive Reactance

Facts About Capacitance Capacitance stores electric energy. W = 0.5CV2 The dielectric material blocks current flow between the plates of a capacitor. The base unit of capacitance is the farad. Most electrolytic capacitors are polarized. A capacitor’s opposition to current is called reactance. XC = 1/(6.28fC) The ohm is the base unit of reactance. Capacitance causes current to lead voltage by 90°.

Construction of a Capacitor Lead Plate Dielectric Plate Lead The plates and leads are conductors. The dielectric is an insulator.

Charging a Capacitor - Current flows and the capacitor charges + 15 V - + until its voltage equals the source voltage. 15 V At this time the current stops. 15 V Time IC VC Notice that I is maximum when V is minimum and visa versa. Imax is very large when C is large and a high-current source is used.

Capacitor-Current Quiz The ____ of a capacitor is an insulator. dielectric The base unit of capacitance is the ____. farad The capacitor current ____ as the capacitor voltage increases. decreases When charged, the capacitor voltage equals the ____ voltage. source Charging current is controlled by the value of ____ and the current capacity of the source. capacitance

Electric Field of a Charged Capacitor Lead Plate First, construct a capacitor and note its parts. + + + + + + + + + + + Next, charge the capacitor and observe the electric field. Dielectric material - - - - - - - - - - - Lead Plate The electric field ( ) stresses the dielectric material.

Stressed Dielectric Material Lead Plate - - - - - - - - - - - - - + + + + + + + + + + + + + + - The distorted orbital paths increase the energy level of the electrons. The capacitor stores energy in its distorted dielectric material.

The next slide shows how rapidly this capacitor can be discharged. Energy Stored In A Capacitor This 5000-μF capacitor is charged to 100 V. The stored energy is: W = 0.5CV2 = 0.5 x .005 x1002 = 25 J This is the amount of energy used by a 100-W light bulb in 0.25 s. The next slide shows how rapidly this capacitor can be discharged.

Click on the image to run the display. Click on the picture to see the discharge again. The next slide estimates the power delivered by the capacitor.

Estimated Power Delivered by the Capacitor P = W / t Estimated time to discharge is about 25 ms. Calculated energy is 25 joules. P = 25J / 0.025s = 1000 W A fully loaded 1-hp motor requires less power than this! Summary: A capacitor can furnish a large amount of power for a very short period of time.

Physical Factors Affecting Capacitance Plate area More capacitance Spacing of plates Less capacitance Mica Air Dielectric material More capacitance

Capacitor-Value Quiz A charged capacitor produces a(n) ____ ____ between its plates. electric field A charged capacitor stores energy in its ____. dielectric Charging a capacitor increases the energy level of the ____ in the dielectric. electrons Increasing the plate area ____ the capacitance. increases Increasing the distance between the plates _____ the capacitance. decreases

Action of a Filter Capacitor Pulsating dc before filtering V t Pulsating dc before filtering V t After filtering

Electrolytic Capacitor Venting plug on this end This capacitor is about to be reverse- connected to a 15-V dc supply. Watch the venting plug in this series of slides.

Reverse voltage has been applied for about 25 seconds. Notice the venting plug is being pushed out. The next slide shows the last 5 seconds of the life of this capacitor.

Please wait for the image to load and display. Watch the venting plug. To rerun the display, click again on the image.

Telephoto view after the smoke has cleared Telephoto view after the smoke has cleared. (For protection, the capacitor was under a piece of glass.)

RC Time Constant -- Charge 100 % of source voltage 1 2 3 4 5 Time constants After 1 T, the capacitor is 63.2 % charged. After 2 T, the capacitor is 86.5 % charged. After 3 T, the capacitor is 95.0 % charged. After 4 T, the capacitor is 98.2 % charged. After 5 T, the capacitor is 99.3 % charged. The capacitor is essentially charged after 5 T.

RC Time Constant -- Discharge 100 % of capacitor voltage 36.8% 13.5% 5.0% 1.8% 0.7% 1 2 3 4 5 Time constants After 1 T, the capacitor is 63.2 % discharged. After 2 T, the capacitor is 86.5 % discharged. After 3 T, the capacitor is 95.0 % discharged. After 4 T, the capacitor is 98.2 % discharged. After 5 T, the capacitor is 99.3 % discharged. The capacitor is essentially discharged after 5 T.

Energy Transfer in a Capacitor Circuit V I - + - + During the first quarter of the cycle, the current decreases as the voltage increases. The source is providing the energy needed to charge the capacitor. When the voltage reaches its peak value, there is no current.

Energy Transfer in a Capacitor Circuit Second quarter-cycle I V - + + - During the second quarter-cycle, the capacitor returns its energy to the source. Notice that the current has changed direction. Also notice that the current is now increasing while the voltage is decreasing.

Energy Transfer in a Capacitor Circuit Third quarter-cycle I V - + - + During the third quarter-cycle, the source provides the energy to charge the capacitor. Notice that the current has not changed direction. It is now decreasing while the voltage is increasing.

Energy Transfer in a Capacitor Circuit Fourth quarter-cycle I V - + - + During the fourth quarter-cycle, the capacitor returns its energy to the source. Notice that the current has changed direction. Also notice that the current is now increasing while the voltage is decreasing.

Capacitor-Action Quiz A filter capacitor changes pulsating dc into ____ dc. fluctuating After one time constant a capacitor is ____ % charged. 63.2 A capacitor is essentially charged after ____ time constants. five In an ac circuit, a capacitor returns energy to the source ____ each cycle. twice With an ac source, the capacitor voltage ____ while the capacitor current increases. decreases

Voltage Distribution in Series Capacitors 2 mF 40 V 4 mF 20 V 2 mF 40 V 4 mF 20 V In either a dc or an ac series circuit, the smallest capacitor develops the most voltage. The voltage distributes in inverse proportion to the capacitance.

Current Distribution in Parallel Capacitors 60 V 2 mF 2 A 4 mF 4 A Peak charging I 60 V 2 mF 0.2 A 4 mF 0.4 A In either a dc or an ac parallel circuit, the largest capacitor draws the most current. The current distributes in direct proportion to the capacitance.

Capacitive Reactance and Capacitance kW W mA mV V A + V A W COM - d c a c 2 mF 40 V 100 Hz 40 V 1mF 100 Hz Measure the current when C is 2 mF. Next, calculate XC. XC = VC / IC = 40 V / 50.24 mA = 796 W Measure the current when C is 1 mF. Then, calculate XC. XC = 40 V / 25.12 mA = 1592 W Notice that XC is inversely proportional to C.

Capacitive Reactance and Frequency kW W mA mV V A + V A W COM - d c a c 2 mF 40 V 100 Hz 40 V 2mF 50 Hz Measure the current when f is 100 Hz. Next, calculate XC. XC = VC / IC = 40 V / 50.24 mA = 796 W Measure the current when f is 50 Hz. Then, calculate XC. XC = 40 V / 25.12 mA = 1592 W Notice that XC is inversely proportional to f.

Relaxation Oscillator Circuit NE-2 NE-2 When power is applied, the capacitor charges to the firing voltage of the NE-2 and produces part of the sawtooth waveform. When the NE-2 fires, the capacitor discharges through the NE-2, the source sends current through the the NE-2 and the resistor, and the rest of the sawtooth waveform is produced. Then the cycle starts over.

Capacitor-Circuit Quiz In a series capacitor circuit, the smallest capacitor develops the ____ voltage. most In a parallel capacitor circuit, the smallest capacitor draws the ____ current. least Increasing capacitance ____ reactance. decreases Increasing frequency ____ reactance. decreases Circuit current in a capacitor circuit will ____ when the frequency is decreased. decrease The reactance of a 2 mF capacitor at 200 Hz is ____ ohms. 398

REVIEW Capacitor Terminology Use of Capacitors Capacitors in Ac and Dc Circuits Series and Parallel Capacitors Time Constants Capacitive Reactance