1. Capacitors
Devices used to store charge

2. Capacitors
Devices used to store charge
Useful to deliver large short “pulse” of charge

3. Capacitors
Amount of charge depends on capacitor design and applied voltage +Q -Q VC + - VB

4. Capacitance
C= 𝑄 𝑉 +Q -Q VC + - VB

5. Example: A parallel plate capacitor-σ d +σ

6. Example: Parallel plates of dimensions, 3 cm x 4 cm are separated by a distance of 0.5 mm. The plates are connected to a battery with a potential difference of 12 V.
a. Determine the capacitance of the plates.
b. Determine the electric field between the plates.
c. Determine the charge on the plates.

7. Example: A coaxial cable capacitor

8. Example: A coaxial cable capacitor
𝐶 𝐿 = 2 𝜋 𝜖 0 ln 𝑏 𝑎
An Application: Determining the distance to the damaged section of a buried cable.

9. Example: Concentric spheres

10. Example: Isolated sphere

11. Capacitors in Circuits
Consider capacitors connected in parallel. C1 C2 C3 VB

12. Capacitors in Circuits
Consider capacitors connected in series. C1 C2 C3 VB

13. Capacitors in Circuits
Parallel
Series
Capacitance
𝐶 𝑇 = 𝐶 𝑖
1 𝐶 𝑇 = 𝐶 𝑖
Potential Difference
𝑉 𝑇 = 𝑉 𝑖
𝑉 𝑇 = 𝑉 𝑖
Charge
𝑄 𝑇 = 𝑄 𝑖
𝑄 𝑇 = 𝑄 𝑖

14. Example: Three identical capacitors with capacitance, C, are connected as illustrated. Determine the total capacitance of the combination.

15. Example: Three identical capacitors with capacitance, C, are connected as illustrated. Determine the total capacitance of the combination.

16. Example: For the capacitor system shown, C1 = 3C, C2 = C and C3 = 2C.
a. Find the equivalent capacitance.
b. Find the charge on each capacitor
(From Exam I, Fall 2017) C1 V0 C2 C3