Physics 232C Topic 16c Capacitance and Capacitors Physics 232C Capacitors Capacitors Q d symbol for capacitor when used in electric circuit A capacitor is a device with two conductors that can store charge and energy It can quickly release the charge if given the opportunity Q If charged the two conductors have equal and opposite charge Q and Q The magnitude of the charge stored Q is proportional to the potential difference V the proportionality constant C is called the capacitance Often C is given in terms of F 10 6F nF 10 9F or pF 10 12F C Q V Q CV C has units of C V or Farad F Physics 232C 1 2 1 Parallel Plate Capacitor Parallel Plate Capacitor Capacitance is a property of the capacitor It only depends on a capacitor s area distance between its plates and the material between the conducting plates We ll address the material between the plates later in this chapter The capacitance does not change even if Q or V change Q d Q Q CV How do we make a capacitor How do we place charge on a capacitor 0A d 0 8 85x10 12 F m C Physics 232C Some Other Circuit Element Some Other Circuit Element Circuit elements in addition to capacitors Wires connect different elements of a circuit together We ll almost always consider these to be perfect conductors Batteries a charge pump Direction of charge motion is that of positive charge Pumps charge q from lower U to higher U The work done by the battery converts chemical energy to electric potential energy U qVb W battery q V battery e U q U 0 Physics 232C U increases U decreases 3 4 2 Some Other Circuit Element Some Other Circuit Element Can charge a capacitor by connecting it to a battery or some other source of electric potential difference also referred to as an EMF source Charge is pumped the negative plate of the capacitor to the positive plate The charge on the capacitor is Q Positive plate has Q Negative plate has Q Capacitor electric potential V capacitor V battery Charge movement ceases when the voltage across the capacitor equal the voltage of the EMF source battery voltage Physics 232C A Capacitor and a Battery A Capacitor and a Battery Use a battery to charge the capacitor so Vc Vb What stays constant Capacitor connected to a battery Potential VC stays constant VC Vb of the battery but Q will change if C changes Disconnect battery Isolated Capacitor Charge Q stays constant no place for charge to go but the potential VC will change if C changes Q CCV C 0A d C only changes if change the area A of the plates the distance d between them or the material between them changes Physics 232C 5 6 3 Physics 232C Example 16c Capacitors Physics 232C Concept Check 1 Concept Check 1 If the potential difference across a capacitor is doubled what happens to its capacitance A Doubles B Halves C Stays the same D Not enough info Physics 232C 7 8 4 Concept Check 2 Concept Check 2 A parallel plate capacitor with area A and distance d between its plates is charged up by a battery but is then disconnected What happens to the capacitor s potential VC if the area of the plates is doubled Physics 232C 9 Concept Check 3 Concept Check 3 A parallel plate capacitor with area A and distance d between its plates is charged up to 20 V using a battery which is then disconnected What happens to the capacitor s potential VC if the distance between the plates is then doubled d d A 40 V B 20 V C 10 V D 0 V E 20V Physics 232C 10 5 Concept Check 4 Concept Check 4 A parallel plate capacitor with area A and distance d between its plates is connected to a 20 V battery What happens to the capacitor s potential VC if the area of the plates is doubled d A 40 V B 20 V C 10 V D 0 V E 20V Physics 232C 11 Parallel Plate Capacitor Parallel Plate Capacitor Two parallel plates each of area 4 52 cm2 are separated by 1 50 mm The space between the plates is filled with air A voltage of 8 45 V is applied between the plates A Calculate the magnitude of the electric field between the plates B Calculate the amount of the electric charge stored on each plate Physics 232C 12 6 Physics 232C Topic 16d Capacitors Energy and Dielectrics Physics 232C 13 Energy of a charged capacitor Energy of a charged capacitor If you know the charge Q and the potential difference V of the two plates of a capacitor then you can find the stored potential energy UC From the definition of potential UV Q You might guess that cU QV WRONG Physics 232C 14 Energy is stored in the electric field 7 Energy of a charged capacitor Energy of a charged capacitor U qV does give the energy to move a charge q from one plate to the other but only for the FULLY charged case Consider the other extreme there was no electric field when the first charge was moved so it did not require any energy work to do it We need to use the average potential difference V U C 1 2 QV C Q CCV U c QV 2 CV C 1 2 1 2 1 2 Q 2 C Physics 232C 15 Parallel Plate Capacitor Parallel Plate Capacitor Plates have area A and separated by distance d If the space is replaced by an insulating material the constant 0 must be replaced by 0 where kappa is the dielectric constant for that material relative to vacuum 0 8 85x10 12 F m C 0A d Assumes the area between the plates is a vacuum empty space C 0A d 1 for vacuum Physics 232C 16 8 Why does inserting material between Why does inserting material between the plates matter the plates matter Applying a voltage Molecules in the material can be polarized Forming dipoles Dipoles align with the field caused by Q on plates Negative plate attracts the positive end of the dipoles The positive plate attracts the negative end of the dipoles Superposition of two fields 1 The field due to the charge on the capacitor s plate 2 The field due to the alignment of the dipoles opposite direction Physics 232C 17 Why does inserting material between Why does inserting material between the plates matter 2 the plates matter 2 Superposition of two fields Field due to the charge on the capacitor plates Field due to the induced charge separation of the dipoles Net field is reduced The result of the dielectric is that E is reduced by a factor of 1 E E Uniform E field V Ed Therefore V V Since C Q V C will increase C C C 0A d Physics 232C 18 9 Some Dielectric Constants Some Dielectric Constants C 0A d Can increase capacitance by either increasing the area decreasing …