PH 203 Professor Lee Carkner Lecture 8 Capacitors PH 203 Professor Lee Carkner Lecture 8

Circuits A potential difference produces work Moving charges can do things e.g. light lightbulbs, induce movement in motors, move information etc. We will examine the key components of electric circuits Up first, the capacitor

Battery The source of potential difference in a direct current (DC) circuit is a battery If we connect one end of a wire to the positive terminal and the other end to the negative terminal, the electrons in the wire will move often called a voltage it just provides the potential to move the electrons that are already in the wire + -

Capacitance Not to be confused with a battery which doesn’t store charge but rather makes charge move This intrinsic property is called capacitance and is represented by C

Capacitance Defined The amount of charge stored by a capacitor is just: Q = C DV C = Q/DV The units of capacitance are farads (F) 1 F = 1 C/V Typical capacitances are much less than a farad: e.g. microfarad = mF = 1 X 10-6 F

Simple Circuit Battery (DV) connected to capacitor (C) The capacitor experiences potential difference of DV and has stored charge of Q = C DV - + Q + - DV

Connections When connecting things to a battery the arrangement can be in series or parallel Series with potential source connected to each end of line Parallel each element has the same potential 1 2 3 DV V1 + V2 + V3 = DV 1 2 3 DV V1 = V2 = V3 = DV

Junctions How can you tell if capacitors are in series or parallel? A place where the current has to split If you can’t draw a path from one capacitor to the other without hitting a junction, they are in parallel C1 C2 + - DV

Capacitors in Parallel Potential difference across each is the same (DV) Total stored charge is the sum (Q = Q1 + Q2) But: Q = CeqDV Ceq = C1 + C2 C1 C2 + - DV

Capacitors in Series Charge stored by each is the same (Q) Equivalent capacitor also has a charge of Q Since DV = Q/C: The equivalent capacitance is: 1/Ceq = 1/C1 + 1/C2 C1 C2 - - + + + - DV

Capacitors in Circuits Remember series and parallel rules extend to any number of capacitors Keep simplifying until you find the equivalent capacitance for the whole circuit

Capacitor Info A capacitor generally consists of two metal surfaces Maintaining a potential difference across the plates causes the charge to separate Electrons are repelled from the negative terminal and end up on one plate Electrons are attracted to the positive terminal and are lost by the second plate Plates can’t touch or charge would jump across

Finding Capacitance We will enclose one plate with a Gaussian surface But for the special case of our capacitors: The plate has a charge q Thus EA = q/e0 q = e0EA q = CV = e0EA C = e0EA/V

Parallel Plate What is the relation between E and V for two parallel plates? But E is constant between the plates and ∫ ds = d, the distance between the plates C = e0A/d

Permittivity e0 = Cd/A So we can write: e0 = 8.85 X 10-12 F/m and think of e0 as being the “capacitor constant”

Using Capacitors Capacitors store energy Generally only for short periods of time Useful when you need a quick burst of energy Defibrillator, flash Since capacitance depends on d, can also use capacitance to measure separation

Next Time Read 25.5-25.8 Problems: Ch 25, P: 6, 9, 14, 26, 36

The potential energy of two like charges a distance a apart is x The potential energy of two like charges a distance a apart is x. The potential energy of two like charges a distance 2a apart is y. What is the total potential energy of the system? A x y 4x-4y 4x-2y

If the other three charges were already fixed in place, how much work would you have to do to bring charge A into place from infinity? A You would have to do positive work The work would equal zero You would do “negative work”, the charge would move in on its own The work would first be positive, then negative You cannot tell without knowing the value of “a”