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## Materials for Lecture

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**Materials for Lecture**• Poling cards • Demos: http://www.physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm • J4-01 • J4-22 • J4-51 TESTI N G Animations courtesy of: http://webphysics.davidson.edu/Applets/Applets.html Sarah Eno**Capacitors**Fields near point charges is all well and good, but let’s do something practical! Capacitors are found in all electric circuits. Capacitor Industries, Inc Chicago, IL Sarah Eno**The charges are held together on the plates by their**attraction. Capacitors A capacitor is a way of storing charge. The symbol for a capacitor in a schematic for an electrical circuit shows basically what it is: two plates with a gap. (often want to store charge so that it can provide current) Sarah Eno**Storing Charge**Let’s think about storing charge… Often, you want to store as much charge as possible, while avoiding large (dangerous) voltages For a fixed voltage, you can increase the charged stored by increasing A or decreasing d Sarah Eno**Capacitance**Or the charge you can store per volt is related to the geometry of the plates and the gap Capacitance is the amount of charge you can store per volt, or Q/V. Farad=coulomb/volt Sarah Eno**Increasing Area**Sarah Eno**Test Yourself**Demo j4-01 • I’m going to charge these plates to 1000 V. I’m going to remove the charger, then I’m going to move them apart. As I move them, will the voltage • Increase • Decrease • Stay the same Sarah Eno**Example**What would be the area of a capacitor with a gap of ½ mm to have a capacitance of 1 farad? Sarah Eno**Example**Air breaks down and conducts for an electric field strength of 3x106 V/m. How many volts can it hold if it has a gap of 1mm? Capacitors come with voltage ratings. Cheap capacitors can typically hold 50 V. Sarah Eno**The Gap**• What if I stick something inside the gap? • Maybe something made of molecules that are electric dipoles… • ceramics • mica • polyvinyl chloride • polystyrene • glass • porcelain • rubber • electrolyte (glyco-ammonium borate, glycerol-ammonium borate, ammonium lactates, etc dissolved in goo or paste) Dielectric material Sarah Eno**Inside: Dipoles**Electric Dipole moments in random directions Put a charge on the plates. The charge creates an electric field. Dipole moments try to align with the field. Sarah Eno**2**3 1 5 6 4 11 7 9 8 10 12 Capacitors • 365 pf, 200V, air variable • 0.25 mF, 3000V, mineral oil • 21000 mF, 25 V, electrolytic • 20 pF, 100 V, air variable • 2 mF, 400 V, polystyrene • 100 mF, 12 V, electrolytic • 10 pf, 200 V, glass/air • 0.1 mF, 10 V, ceramic • 0.1 mF, 1 kV, ceramic • 0.33 mF, 400 V, mylar • 100 pF, 2kV, ceramic • 1000 pF, 200V, silver mica 1) Tune radios, 2) filter HV, 3) power supply filter, 4) tune rf, 5) audio 6) audio, 7) vhf/uhf, 8) audio, 9) audio, 10) audio, 11) high power rf, 12) precision rf Sarah Eno**Test Yourself**• Will the field between (and thus the voltage between) the plates be • Larger • Smaller • The same • As without the dielectric? Do j4-22 Sarah Eno**Inside: Fields**The field goes down. So, the amount of charge you can put on for 1 volt is larger. So, the capacitance goes up. A certain fraction of the field is “canceled”. E=E0/k. V=V0/k. C=kC0 Sarah Eno**Dielectrics**Material k Breakdown field (106 V/m) --------------------------------------------------------------- Air 1.00059 3 Paper 3.7 16 Glass 4-6 9 Paraffin 2.3 11 Rubber 2-3.5 30 Mica 6 150 Water 80 0 Sarah Eno**Example**What area would a capacitor with a 0.5 mm gap have to for a capacitance of 1 farad if it had a dielectric constant (k) of 10? Found earlier that without dielectric, need an area of 56x106 m2. So, reduce this by 10 to 56x105 m2 Sarah Eno**Example**A typical capacitor has a capacitance of 10 mF, a gap of 0.1 mm, and is filled with a dielectric with a dielectric strength of 10. What is the area? Sarah Eno**Energy Stored**How much work to move some this charge onto the capacitor? Amount of work to charge from scratch. Sum (integral) up the contributions to bring each charge Sarah Eno**Energy Stored**But, Q is hard to measure Sarah Eno**Simple Circuits**Let’s try our first simple circuit Sarah Eno**Capacitors with a Battery**An “ideal” battery is a source of constant voltage. Though it is done using properties of metal, ions, etc, you should think of it as containing a fixed E field. Charge on one side is at a higher potential than the other Sarah Eno**Batteries**Students have many misconceptions about batteries, which lead to serious difficulties in making predictions about circuits. Batteries are not charged. They do not contain a bunch of electrons, ready to “spit out” Batteries are not current sources. They don’t put out a constant current. Sarah Eno**Ground**Zero volt point. Reservoir of electrons. Can take and give electrons easily. Sarah Eno**Circuits**Remember: it takes no work to move an charge through a conductor. The potential does not change! (for an ideal conductor… since only a “superconductor” is an ideal conductor, this is only mostly true for copper, gold, etc) Sarah Eno**Test Yourself**• When I close the switch will the voltage across the battery • Go down because charge leaves the battery to go to the capacitor • Go up because the battery will get additional charge from the capacitor • Stay the same because the voltage across a battery always stays the same Sarah Eno**Battery + Capacitor**Sarah Eno**Example**What is the charge on a 1 mF capacitor attached to a 1.5 V battery? How many electrons is that? Sarah Eno**Capacitor Circuits**• If you have more than 1 capacitor in a circuit, two basic ways to arrange them • parallel • series Sarah Eno**Parallel Circuits**Connected in Parallel • How will the voltage across them compare? • It will half. The voltage from the battery will be divided between the two • It will double. Because there will be two capacitors charged • It will be the same. The voltage is always the same. Sarah Eno**Parallel Circuits**How does the charge compare? Sarah Eno**Parallel**Twice the charge for the same voltage. Effectively increasing the area of the capacitor Sarah Eno**Parallel**If you replaced the 2 capacitors with 1 capacitor, what capacitance would it have to have in order to have the same voltage and the same charge -> effective capacitance of the system Sarah Eno**Series**• How will the voltage across them compare? • It will half. The voltage from the battery will be divided between the two • It will double. Because there will be two capacitors charged • It will be the same. The voltage is always the same. The voltage across each is 1/2. That means the charge on each is ½ compared to 1 capacitor circuit. Sarah Eno**Series**Its like you have twice the gap. The effective capacitance goes down. Sarah Eno**Series in General**Sarah Eno**Check**Sarah Eno**Hints for Capacitors**• remember the voltage across a battery is fixed • remember voltage does not change along a wire • look for parallel and series combinations, and calculate the equivalent capacitance. Sarah Eno**Example**What is the charge on each cap? What is the voltage across each cap? • Look for series and parallel combinations. Calculate equivalent capacitance. Replace. Repeat until have 1 cap. • Then work backwards Sarah Eno**Example**Sarah Eno**Example**Before the dielectric is added, the capacitance is C0. What is the capacitance afterwards? Picture it as two caps in series, each with a gap d/2 and therefore capacitance 2C0. When add dielectric, each capacitance goes up a factor k Sarah Eno**Test Yourself**• Which capacitor has the biggest charge? • 1mF • 0.2 mF • 0.6 mF • They all have the same charge • None of the above Sarah Eno**Example**What is the equivalent capacitance? .6 and .2 are in parallel. Add them to get .8 The 1 and the “.8” are in series. Sarah Eno**Fun**Another use for capacitance Do j4-51 Sarah Eno**Hints for Capacitor Problems**Sarah Eno