Electric Potential and Capacitors

1. Electric Potential and Capacitors Mr. Kamanda

2. Electric Potential & Capacitors • At the end of this class, SWBAT: • Understand the concept of potential and electrical work done. • Determine electric potential for due to one or more charges. • Calculate potential difference between two points. • Calculate electric potential energy. • Calculate the capacitance of a capacitor. • Calculate equivalent capacitance. • Calculate energy stored in a capacitor.

3. Introduction to Lines of Potential  The diagram below represents students standing on bleachers in the gym. The height of the bleachers is given and the mass of the students is given. g= 10m/s2

4. Introduction to Lines of Potential 3600 J 4500 J  The diagram below represents students standing on bleachers in the gym. The height of the bleachers is given and the mass of the students is given. 800 J 2000 J 700 J 1600 J 0 J 0 J Their Eg to mass ratio is a constant and the value increases with height.

5. Electric Potential • Electric Potential allows us to express how much energy a charge would have if placed at a particular position within an electric field. • Just as work is done when a mass is moved from one level to another in the gravitational field, work is also done when a charge moves in an electric field. • The work done in an electric field appear as a change in the potential energy of the charge.

6. Electric Potential

7. Potential Energy Consider a positive test charge A placed in the electric field of another positive charge. • It will move towards B. • A is said to have a higher potential than B. • The potential energy at a point in an electric field is defined as the work required to moves the charge form infinity to that point. • PE = UE =

8. Potential The electric potential at a point is defined as the work done in bringing unit charge from infinity to that point. V = = Electric potential is a scalar quantity. The electric potential at a point due to a collection on charges is: V = The SI units for potential are joules per coulomb or Volts (V). 1 V  1 J/C

9. Problems • What is the potential at 3.0 cm from a point charge of 5.0 x 10-8 C? • A 12 C and a – 8 C are separated by a distance of 0.70 m. What is the potential at their midpoint?

10. Electric Potential Difference • The potential difference between two points in an electric field is defined as the work required to move a unit positive test charge moved from the point of lower potential to that of a higher potential. • Potential difference is sometimes referred as Voltage.

11. Potential difference and Field Strength • E v1 d v2 • If a charge moves a distance in a uniform electric field, E, the change in potential energy is: • And the potential difference is: = Hence we can write the field strength E, as Another unit of Electric field is volts per meter ( V/m)

12. The Electron Volt • This is a unit of energy commonly used in atomic and nuclear physics. • The electron volt is defined as the energy that an electron (or Proton) gains when accelerated through a potential difference of 1 V. 1 eV =1.60 X 10 -19 J

13. Equipotentials • Equipotentialsare contour maps of the electric potential. Equipotentials surfaces are surfaces on which all points are at the same potentials.

14. The electric field lines are perpendicular to the equipotential lines.

15. Capacitors A capacitor is an electric device that stores charge. A capacitor is basically two parallel conducting plates with air or insulating material in between. Electrical symbol of capacitor:

16. Capacitance of a capacitor • The ability of a capacitor to store charge is measured by its’ capacitance, C. Q is the charge stored on the capacitor plates, and V is the voltage applied across the plates. • The SI unit of Capacitance is farads (F). • We will use smaller unit of Capacitance in the range: 1F = 1 x 10-6 F to 1 pF = 1 X 10 -12 F

17. Parallel-Plate Capacitor • The capacitance of a parallel-plate capacitor depends on its’ geometric arrangement. • If the overlapping area of the plates is A, their separation is d and air is between them, then the capacitance is: • is a constant called the permittivity of free space. • = 8.85 X10-12 C2/N.m2

18. Problems A parallel-plate capacitor has an area of 2.0 cm2, and the plates are separated by 2.0 mm. • What is the capacitance? • How much charge does this capacitor store when connected to a 6.0 V Battery?

19. Problems Assume Earth and a cloud layer 800.0m above the Earth can be treated as a parallel-plate capacitor. • If the cloud layer has an area of 1.00 x10-6 m2,what is the capacitance? • If an electric field strength of 2.0 x 106 N/C causes the air to conduct charge (lightning), what charge can the cloud hold?

20. Combining Capacitors in Parallel

21. Parallel Combination

22. Combining Capacitors in Series

23. Series Combination

24. Collecting equations: Q = C1 V1 Q = C2 V2 Q = C3 V3 Vab= V = V1 + V2 + V3. Q = CpV Substituting for V1, V2, and V3: Substituting for V: Dividing both sides by Q:

25. Series Combination • Generalizing: Ex: Three capacitors C1 = 3.00 F, C2 = 4.50F and C3 = 9.00 F are connected together. Find the effective capacitance (a) if they are connected in parallel, and (b) if they are connected in series.

27. Energy Stored in a Charge Capacitor • The transferring of charge on to the plates of a capacitor requires work to be done by the battery. • This work is stored in the capacitor as electrical energy. • The energy stored is given by: • CV2

28. Problem Calculate the energy stored in each case in the previous problem if they capacitors are connected to a 12.0 V battery.

29. Summary • Potential, Potential energy and potential difference: • Electric field and Potential gradient • Equipotentials • Capacitors and Capacitance • Equivalent capacitance and energy stored by a capacitor.