General Physics 2: Capacitor & Capacitance PDF

GENERAL PHYSICS 2: CAPACITOR & MR. GENESIS E. ALMEÑE LESSON 6 CAPACITANCE JANUARY 21, 2024 CAPACITOR & CAPACITANCE A CAPACITOR IS A DEVICE THAT STORES ELECTRIC POTENTIAL ENERGY AND ELECTRIC CHARGE. TO MAKE A CAPACITOR, JUST INSULATE TWO...

GENERAL PHYSICS 2: CAPACITOR & MR. GENESIS E. ALMEÑE LESSON 6 CAPACITANCE JANUARY 21, 2024 CAPACITOR & CAPACITANCE A CAPACITOR IS A DEVICE THAT STORES ELECTRIC POTENTIAL ENERGY AND ELECTRIC CHARGE. TO MAKE A CAPACITOR, JUST INSULATE TWO CONDUCTORS FROM EACH OTHER. TO STORE ENERGY IN THIS DEVICE, TRANSFER CHARGE FROM ONE CONDUCTOR TO THE OTHER SO THAT ONE HAS A NEGATIVE CHARGE AND THE OTHER HAS AN EQUAL AMOUNT OF POSITIVE CHARGE. WORK MUST BE DONE TO MOVE THE CHARGES THROUGH THE RESULTING POTENTIAL DIFFERENCE BETWEEN THE CONDUCTORS, AND THE WORK DONE IS STORED AS ELECTRIC POTENTIAL ENERGY. CAPACITOR & CAPACITANCE CAPACITORS HAVE A TREMENDOUS NUMBER OF PRACTICAL APPLICATION DEVICES SUCH AS ELECTRONIC FLASH UNITS OF PHOTOGRAPHY, PULSED LASER, AIR BAG SENSORS FOR CARS, AND RADIO AND TELEVISION RECEIVERS. FOR A PARTICULAR CAPACITOR, THE RATIO OF THE CHARGE ON EACH CONDUCTOR TO THE POTENTIAL DIFFERENCE BETWEEN THE CONDUCTOR IS CONSTANT, CALLED THE CAPACITANCE. THE CAPACITANCE DEPENDS ON THE SIZES AND SHAPES OF THE CONDUCTORS AND ON THE INSULATOR MATERIAL (IF ANY) BETWEEN THEM. COMPARED TO THE CASE IN WHICH THERE IS ONLY VACUUM BETWEEN THE CONDUCTORS, THE CAPACITANCE INCREASES WHEN AN INSULATING MATERIAL (A DIELECTRIC) IS PRESENT. CAPACITOR & CAPACITANCE IN MOST PRACTICAL APPLICATIONS, EACH CONDUCTOR INITIALLY HAS ZERO NET CHARGE AND ELECTRONS ARE TRANSFERRED FROM ONE CONDUCTOR TO THE OTHER; THIS IS CALLED CHARGING THE CAPACITOR. THEN THE TWO CONDUCTORS HAVE CHARGES WITH EQUAL MAGNITUDE AND OPPOSITE SIGN, AND THE NET CHARGE ON THE CAPACITOR AS A WHOLE REMAINS ZERO. IN A CIRCUIT DIAGRAMS A CAPACITOR IS REPRESENTED BY EITHER OF THESE SYMBOLS: CAPACITOR & CAPACITANCE IN EITHER SYMBOL THE VERTICAL LINES (STRAIGH OR CURVED) REPRESENT THE CONDUCTORS AND THE HORIZONTAL LINES REPRESENT THE WIRES CONNECTED TO EITHER CONDUCTOR. ONE COMMON WAY TO CHARGE A CAPACITOR IS TO CONNECT THESE TWO WIRES TO OPPOSITE TERMINALS OF A BATTERY. ONCE THE CHARGES +Q AND –Q ARE ESTABLISHED ON THE CONDUCTORS, THE BATTERY IS DISCONNECTED. THIS GIVES A FIXED POTENTIAL DIFFERENCE (𝐕𝐀𝐁 ) BETWEEN THE CONDUCTORS (THAT IS, THE POTENTIAL OF THE POSITIVELY CHARGE Conductor a WITH RESPECT TO THE NEGATIVELY CHARGE Conductor b) THAT IS EQUAL TO THE VOLTAGE OF THE BATTERY. CAPACITOR & CAPACITANCE THE ELECTRIC FIELD AT ANY POINT IN THE REGION BETWEEN THE CONDUCTORS IS PROPORTIONAL TO THE MAGNITUDE Q OF THE CHARGE EACH CONDUCTOR. IT FOLLOWS THAT THE POTENTIAL DIFFERENCE (VAB ) BETWEEN THE CONDUCTORS IS ALSO PROPORTIONAL TO Q. IF WE DOUBLE THE MAGNITUDE OF THE CHARGE ON EACH CONDUCTOR, THE CHARGE DENSITY AT EACH POINT DOUBLES, THE ELECTRIC FIELD AT EACH POINT DOUBLES, THE POTENTIAL DIFFERENCE BETWEEN CONDUCTORS DOUBLES; HOWEVER THE RATIO OF CHARGE TO POTENTIAL DIFFERENCE DOES NOT CHANGE. CAPACITOR & CAPACITANCE THIS RATIO IS CALLED THE CAPACITANCE (C) OF THE CAPACITOR: THE SI UNIT OF CAPACITANCE IS CALLED ONE FARAD (1 F), IN HONOR OF THE 19TH CENTURY ENGLISH PHYSICIST MICHAEL FARADAY. 1 FARAD IS EQUAL TO ONE COULOMB PER VOLT (1 C/V). THUS CAPACITANCE IS A MEASURE OF THE ABILITY OF A CAPACITOR TO STORE ENERGY. CALCULATING CAPACITANCE: CAPACITORS IN VACUUM THE SIMPLEST FORM OF CAPACITOR CONSIST OF TWO PARALLEL CONDUCTING PLATES, EACH WITH AREA A, SEPARATED BY A DISTANCE d THAT IS SMALL IN COMPARISON WITH THEIR DIMENSION. WHEN THE PLATES ARE CHARGED, THE ELECTRIC FIELD IS ALMOST COMPLETELY LOCALIZED IN THE REGION BETWEEN THE PLATES. THE FIELD BETWEEN SUCH PLATES IS ESSENTIALLY UNIFORM, AND THE CHARGES ARE UNIFORMLY DISTRIBUTED OVER THE OPPOSING SURFACES. WE CALL THIS ARRANGEMENT A PARALLEL-PLATE CAPACITOR. CALCULATING CAPACITANCE: CAPACITORS IN VACUUM WE WORKED OUT THE ELECTRIC FIELD MAGNITUDE FOR THIS ARRANGEMENT USING THE PRINCIPLE OF SUPERPOSITION OF ELECTRIC FIELD AND GAUSS’S LAW. 𝜎 𝑄 WE FOUND THAT E = ; 𝜎= , SO THE FIELD COULD BE 𝜀0 𝐴 EXPRESSED AS THE FIELD IS UNIFORM AND THE DISTANCE BETWEEN THE PLATES IS d, SO THE VOLTAGE BETWEEN THE TWO PLATES IS CALCULATING CAPACITANCE: CAPACITORS IN VACUUM THE CAPACITANCE C OF A PARALLEL-PLATE CONDUCTOR IN VACUUM IS THE CAPACITANCE DEPENDS ONLY ON THE GEOMETRY OF THE CAPACITOR; IT IS DIRECTLY PROPORTIONAL TO THE AREA A OF EACH PLATE AND INVERSELY PROPORTIONAL TO THEIR SEPARATION d. CALCULATING CAPACITANCE: CAPACITORS IN VACUUM ONE FARAD IS A VERY LARGE CAPACITANCE, AS THE FOLLOWING EXAMPLE SHOWS. IN MANY APPLICATIONS THE MOST CONVENIENT UNITS OF CAPACITANCE ARE MICROFARAD 1 μF = 1 x 10−6 F AND THE PICOFARAD 1 pF = 1 x 10−12 F. FOR EXAMPLE, THE FLASH OF THE UNIT IN A POINT-AND- SHOOT CAMERA USES A CAPACITOR OF A FEW HUNDRED MICROFARADS, WHILE CAPACITANCES IN A RADIO TUNING CIRCUIT ARE TYPICALLY FROM 10 TO 100 PICOFARADS. EXAMPLE 1: PROPERTIES OF A PARALLEL-PLATE CAPACITOR