Lecture 9 Chapter 29 Physics II Capacitors and more Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html
The Geometry of Potential and Field E s dv ds Let s be along an equipotential line, where V=const. So dv=0. So, it is impossible to have an electric field along equipotential lines, E E s equipotent 0 dv ds ial 0 lines
ConcepTest 1 El. Potential/Area Which set of equipotential surfaces matches this electric field? E A) B) C) D) E) F)
Potential of a Conductor V const f i f V V V E ds V 0 f i i V V f i A conductor in electrostatic equilibrium is at the same potential.
The Electric Battery A battery transforms chemical energy into electrical energy. Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. Two electrons get attracted by the ion of Zn leaving behind positively charged electrode Atom of Zn gets dissolved leaving two electrons behind
Capacitor
Capacitor stores energy You can store potential energy by pulling a bow, stretching a spring, etc. A capacitor is a system that stores potential energy in a form of an electric field.
Capacitance (definition) V C The ratio of the charge Q to the potential difference V C is called the capacitance C: The SI unit of capacitance is the farad:
Parallel-plate capacitor In its simplest form, a capacitor consists of a pair of parallel metal plates separated by air/insulating material.
Q Parallel-plate capacitor Let s find capacitance of a parallel-plate capacitor E +Q area A We need to find Q and ΔV: The electric field between the plates is surface charge density d The potential difference between plates: (Eq.28.26) This gives the capacitance: Capacitance is a purely geometric property of two electrodes because it depends only on their surface area and spacing. =
Parallel-plate capacitor We can increase capacitance by increasing area A (by making a roll of metal and insulator
Parallel-plate capacitor/keyboard The keys on most computer keyboards are capacitor switches. Pressing the key pushes two capacitor plates closer together, increasing their capacitance. Capacitors are important elements in electric circuits. They come in a variety of sizes and shapes.
ConcepTest 2 What is the capacitance of these two electrodes? Capacitance A) 8 nf B) 4 nf C) 2 nf D) 1 nf E) Some other value
ConcepTest 3 A parallel-plate capacitor initially has a voltage of 400 V and stays connected to the battery. If the plate spacing is now doubled, what happens? Varying Capacitance I A) the voltage decreases B) the voltage increases C) the charge decreases D) the charge increases E) both voltage and charge change Since the battery stays connected, the potential difference must remain constant! C 0 A d Since, when the spacing d is doubled, the capacitance C is halved. And since Q = C V, that means the charge must decrease. +Q Q 400 V Follow-up: How do you increase the charge?
ConcepTest 4 Varying Capacitance II A parallel-plate capacitor initially has A) 100 V a potential difference of 400 V and is B) 200 V then disconnected from the charging C) 400 V battery. If the plate spacing is now doubled, what is the new value of the D) 800 V voltage? E) 1600 V Once the battery is disconnected, Q has to +Q Q remain constant, since no charge can flow either to or from the battery. C 0 A d Since, when the spacing d is doubled, the capacitance C is halved. And since Q = CV, that means the voltage must double 400 V
Capacitors In Series and Parallel
Combinations of Capacitors In practice, two or more capacitors are sometimes joined together. The circuit diagrams below illustrate two basic combinations: parallel capacitors and series capacitors. The equivalent capacitance is the capacitance of the single capacitor that can replace a set of connected capacitors without changing the operation of the circuit
Real circuit +Q Capacitors in Series Consider three capacitors connected in series. Q Capacitors in series have the same charge, Q. + + Since C 1 C 2 C 3 -Q +Q -Q +Q -Q ΔV 1 ΔV 2 ΔV 3 ΔV + - Equivalent circuit Q C eq ΔV C eq is inserted without changing the operation of the circuit, so Q and ΔV are same as in the real circuit + + Equivalent capacitance of capacitors in series.
Real circuit Capacitors in Parallel Consider three capacitors connected in parallel. Q ΔV, ΔV, ΔV, ΔV Capacitors in parallel have the same potential difference, ΔV = Q is a total charge drawn from the battery Conservation of charge + + Since ; ; ; Equivalent circuit Q C eq ΔV We have replaced 3 capacitors with a equivalent capacitor. C eq is inserted without changing the operation of the circuit, so Q and ΔV are same as in the real circuit + + + + Equivalent capacitance of capacitors in parallel.
ConcepTest 5 Equivalent Capacitor I What is the equivalent capacitance, C eq, of the combination below? A) C eq = 3/2C B) C eq = 2/3C C) C eq = 3C D) C eq = 1/3C E) C eq = 1/2C The 2 equal capacitors in series add up as inverses, giving 1/2C. These are parallel to the first one, which add up directly. Thus, the total equivalent capacitance is 3/2C. o C eq o C C C in series in series In parallel 2 3 2 2 o o C In parallel
What you should read Chapter 29 (Knight) Sections 29.4 29.5
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