Download Capacitance: Understanding Charged Conductors and Stored Energy and more Slides Electrical Engineering in PDF only on Docsity!
2/1/12 1 Chapter 24 Capacitance
- Capacitor is a device that stores electrostatic potential energy.
- A capacitor consists of 2 spatially separated conductors which can be charged to +Q and - Q. 2/1/12 2 Capacitance
- The capacitance is defined as the ratio of the charge on one conductor of the capacitor to the potential difference between the conductors.
- Capacitance is measured in Faradays represented by the letter F which is equal to (coulomb/volt) 2/1/12 3 Capacitance between Parallel Plates
- Calculate the capacitance. We assume + , - charge densities on each plate with potential difference V **:
- +** A d 2/1/12 4 Example What is the capacitance of a parallel plate capacitor made out of two square plates 10 x10 cm^2 separated by 1 mm wide gap? d=1 mm A=0.01 m^2 If we connect 1.5V battery to its plates, how much charge could be stored in this capacitor?
2/1/12 5 Calculating Capacitance
- Put + Q , – Q on the plates.
- Find between the plates i.e., given the charges, using Gauss’ Law
- Find V across the plates 4. Use the definition.
E
V
Q
C =
2/1/12 6 A Cylindrical Capacitor: Step 1
Where R 1 < R 2 << L
2/1/12 7 A Cylindrical Capacitor : Step 2
- The electric field in between the plates is radial. Use a cylindrical shaped Gaussian surface of radius R ( R 1 <R<R 2 ) of length l<<L
∫ S ⋅ = ∫ + ∫ =
o inside Endcaps l Barrel R
Q
EdA EdA E dA ε
2/1/12 8 A Cylindrical Capacitor : Step 3
2/1/12 (^13) Numbers U = 1 2 CV^2 = 1 2 ( 70 μ F ) ( 5000 V ) 2 = 875 J
P =
PE
t
200 J
2 × 10
− 3
s
= 100 kW
short time About 200 J of this is sent through the heart attack victim in 2 milliseconds. http://cache.gizmodo.com/assets/images/ 4/2012/01/41943df714611b001642eadfce4a9e8c.jpg http://www.huffingtonpost.com/2012/01/15/ water-droplets-images_n_1204800.html
