Chapter 24 Capacitance, dielectrics and electric energy storage Basic circuit devices Resistors Capacitors Inductors Power supply (Battery, Generator) Use our knowledge of electric fields, potentials, and energy to describe how capacitors work.

Parallel Plate Capacitor

Active Figure 26.4 (b) When the switch is closed, the battery establishes an electric field in the wire that causes electrons to move from the left plate into the wire and into the right plate from the wire. As a result, a separation of charge exists on the plates, which represents an increase in electric potential energy of the system of the circuit. This energy in the system has been transformed from chemical energy in the battery. Fig 26-4b, p.800

Active Figure 26.4 (SLIDESHOW MODE ONLY)

Potential difference and electric fields in a uniform electric field +Q -Q b d a

Potential difference and electric fields in a uniform electric field +Q -Q b d a The constant of proportionality is called “capacitance.” For a parallel plate capacitor, the capacitance is:

Factors affecting capacitance Size of the capacitor (A, d) Geometric arrangement Plates Cylinders Material between conductors Air Paper Wax

Units of capacitance A Farad is a lot of capacitance. Typical capacitors are “micro, nano, pico-Farad

Capacitance – Isolated Sphere Assume a spherical charged conductor Assume V = 0 at infinity Note, this is independent of the charge and the potential difference

Cylindrical capacitor b +Q on center conducting cylinder -Q on outer conducting cylinder

Capacitance of a cylindrical capacitor b

Example How strong is the electric field between the plates of a 0.80 mF air gap capacitor if they are 2.0 mm apart and each has a charge of 72 mC?

Capacitors in Parallel b

Capacitors in Series a b

Capacitor circuit example 3 V What single capacitor can replace the four shown here? How much charge can the system hold? How much charge is on one of the 2 mF capacitors?

Energy Storage in Capacitors (Like problem 23-50) Change in potential energy while charging capacitor Parallel Plates Concentric Cylinders In General

Alternate Energy Expressions

Energy Density Energy per unit volume: Consider a Parallel Plate Capacitor:

Dielectrics k is the Dielectric Constant - - + + - + + + - - + - A dielectric is a nonconducting material that, when placed between the plates of a capacitor, increases the capacitance Materials with Dipoles that can align with an external electric Field. Dielectrics include rubber, plastic, and waxed paper - - + + - + + + - - + - k is the Dielectric Constant Measure of the degree of dipole alignment in the material

Dielectrics

Example values of dielectric constant “Dielectric strength” is the maximum field in the dielectric before breakdown. (a spark or flow of charge)

Effect of a dielectric on capacitance Potential difference with a dielectric is less than the potential difference across free space Results in a higher capacitance. Allows more charge to be stored before breakdown voltage.

Effect of the dielectric constant Parallel Plate Capacitor Material permittivity measures degree to which the material permits induced dipoles to align with an external field Example modifications using permittivity

Example – Parallel Plate Capacitor +Q What is new capacitance? d A -Q

Dipoles The combination of two equal charges of opposite sign, +Q and –Q, separated by a distance l -Q +Q

Dipoles in a Uniform Electric Field +Q -Q

Work Rotating a Dipole in an Uniform Electric Field +Q -Q

Example P26.9 When a potential difference of 150 V is applied to the plates of a parallel-plate capacitor, the plates carry a surface charge density of 30.0 nC/cm2. What is the spacing between the plates?

Example P26.21 Four capacitors are connected as shown in Figure P26.21. Find the equivalent capacitance between points a and b. Calculate the charge on each capacitor if ΔVab = 15.0 V.

Example P26.27 Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P26.27. Take C1 = 5.00 μF, C2 = 10.0 μF, and C3 = 2.00 μF.

Example P26.35 A parallel-plate capacitor is charged and then disconnected from a battery. By what fraction does the stored energy change (increase or decrease) when the plate separation is doubled? . Therefore, the ,

Example P26.43 Determine (a) the capacitance and (b) the maximum potential difference that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 1.75 cm2 and plate separation of 0.040 0 mm.

Example P26.59 A parallel-plate capacitor is constructed using a dielectric material whose dielectric constant is 3.00 and whose dielectric strength is 2.00 × 108 V/m. The desired capacitance is 0.250 μF, and the capacitor must withstand a maximum potential difference of 4 000 V. Find the minimum area of the capacitor plates.