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Capacitance (II)

Explore capacitance in circuits, symbols, capacitor combinations, effective capacitance calculation, energy storage, and examples of capacitor configurations. Understand parallel and series circuits, energy transfer, and potential differences in capacitors.

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Capacitance (II)

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  1. Capacitance (II) • Capacitors in circuits • Electrostatic potential energy

  2. Capacitors in Circuits Symbols: Capacitor  - + Battery  - + or Switch 

  3. A B A B Capacitor Combinations Parallel Series What is the “effective capacitance” between A & B? A B -Q +Q

  4. C1 C2 C3 Parallel A Q1 Q2 Q3 V -Q1 -Q2 -Q3 B Voltages are the same: V1 = V2 = V3 = … = V Charges add: But…

  5. -Q -Q +Q +Q Series +Q -Q B A C2 C1 C3 Voltages add: Charges are equal: And …

  6. 1uF 4uF b 3uF a 6uF 8uF 2uF Example Find the equivalent capacitance between a and b.

  7. Solution

  8. Example Find the equivalent capacitance between points a and b in the combination of capacitors shown below

  9. Example Consider the circuit shown below, where C1 = 6.00 μF, C2 = 3.00 μF, and ΔV = 20.0 V. Capacitor C1 is first charged by the closing of switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by the closing of S2. Calculate the initial charge acquired by C1 and the final charge on each capacitor.

  10. Solution

  11. Quiz 5 mF a b How does the potential difference Vab between a and b compare to the potential difference Vbc between b and c? 6V 10 mF c • Vab= Vbc • Vab> Vbc • Vab< Vbc

  12. Energy Stored in a Capacitor Remove dq from lower plate and add to upper plate: +q dq -q Increase in P.E., Start at q = 0, finish at q = Q:

  13. Area A +Q s -Q Example What is the energy stored in a parallel-plate capacitor, in terms of the plates’ area and separation?

  14. Example Calculate the energy stored in a 18μF capacitor when it is charged to a potential of 100V.

  15. Example • Three capacitors of 8μF,10μF and 14μF are connected • to the terminals of a 12-volt battery. How much energy • does the battery supply if the capacitors are connected • In series • In parallel

  16. Quiz Conducting spheres and a long wire: A total charge +12 μC is placed on one sphere. The charge will move to the other sphere until • the electric fields on the spheres are equal • the electric potentials on the spheres are equal • the electric charges on the spheres are equal

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