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

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

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

4. Parallel C1C1 C2C2 C3C3 A B V Q1Q1 -Q 1 Q2Q2 -Q 2 Q3Q3 -Q 3 Voltages are the same: V 1 = V 2 = V 3 = … = V Charges add: But…

5. Series Voltages add: Charges are equal: And … +Q -Q +Q -Q +Q -Q C1C1 C3C3 C2C2 A B

6. Example 8uF 4uF 2uF 6uF 1uF 3uF b a 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. Consider the circuit shown below, where C 1 = 6.00 μF, C 2 = 3.00 μF, and ΔV = 20.0 V. Capacitor C 1 is first charged by the closing of switch S 1. Switch S 1 is then opened, and the charged capacitor is connected to the uncharged capacitor by the closing of S 2. Calculate the initial charge acquired by C 1 and the final charge on each capacitor. Example

10. Solution

11. Quiz a b c How does the potential difference V ab between a and b compare to the potential difference V bc between b and c ? 6 V6 V 5  F 10  F A) V ab  V bc B) V ab  V bc C) V ab  V bc

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

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

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 a)In series b)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 A)the electric fields on the spheres are equal B)the electric potentials on the spheres are equal C)the electric charges on the spheres are equal