Storing Electrical Energy Capacitors

Overview Storing electrical charge Defining capacitance Applications Relationships

Storing electrical potential energy Squeeze a spring  stored elastic potential energy Hold magnets together  stored magnetic potential energy Hold electric charges together  stored electrical potential energy

Holding charges Voltage source (e.g., battery) Two conductive plates, separated by a non-conductor called a dielectric

Charging a capacitor When one plate is connected to the voltage source (left plate in this example), an electric field is created, causing electrons to flow from left plate towards positive terminal. Electrons are pulled toward other plate.

Charged capacitor After some time, the potential difference between the capacitor plates is equal to the potential difference from the battery. When V capacitor = V battery, the electrons stop flowing. The capacitor is considered fully charged.

Some applications Storing large amounts of charge for later release e.g., camera flash, defibrillator Computer interface components e.g., touch screen, keyboards Protecting components from surges in direct current e.g., adapters, surge protectors Uninterrupted power supply e.g., power for computers and other electronic devices with changing load requirements In conjunction with resistors, timing circuits e.g., pacemakers or intermittent windshield wipers Etc. Virtually every piece of modern electronics contains capacitors. Read more here:

Quantifying capacitance Strong and uniform electric field between the plates 0 N/C outside the plates 1 st : consider the electric field created by two parallel plates

Recall 2 nd : remember the relationship between strength of the electric field, voltage and distance

Strength of Electric Field Depends on voltage, e.g., battery Depends on separation of charges So, 2V  2E 2d  ½E

Quantifying capacitance 3 rd : draw the connection between charge stored and voltage

Quantifying capacitance Capacitance Measured in units of coulombs per volt, abbreviated as farads 1 farad = the capacitance that can hold 1 coulomb of charge with 1 volt potential difference. 1 F = 1 C / 1 V Named in honor of Michael Faraday, an English scientist (1791 – 1867) who connected fields of electricity and magnetism.Michael Faraday

Typical capacitance

Example The figure at right shows the ratio of charge to voltage of three different capacitors. Which capacitor has the greatest capacitance: A, B, or C? Justify your answer. Q = CV, so C= Q/V. Steeper the slope, bigger the value of C. Line A has the steepest slope and therefore the largest capacitance. Think it through first. Check the solution by moving this box.

Example Try it first. Check the solution by moving this box.

Example Try it first. Check the solution by moving this box.

Factors that affect capacitance Area of plates

Factors that affect capacitance Distance between plates

Factors that affect capacitance Material between plates Chemistry nerds: polar molecules!

Dielectrics Maximum strength of field before dielectric breaks down and charges start flowing

Factors that affect capacitance Area of plates  A  C Distance between plates  d  C Material between plates    C

Quantifying capacitance, part 2

Example A parallel plate capacitor has an area of 1.00 m 2 and a spacing of mm. If the insulator has a dielectric constant of 4.9, what is the capacitance? Try it first. Check the solution by moving this box.

Example In one kind of computer keyboard, each key is attached to one plate of a parallel plate capacitor. The other plate is fixed. The capacitor is maintained at 5.0 V. When the key is pressed down, the top plate moves closer, changing the capacitance and allowing charge to flow again. The circuit detects the change and sends a signal to the computer screen. If each plate is a square of 36.0 mm 2 and the plate separation changes from 4.0 mm to 1.2 mm when a key is pressed, how much charge flows through the circuit? Assume there is air between the plates instead of a flexible insulator.

Example Here’s a hint: consider how the capacitance changes when the key is up and when it is pressed down. Try it first. Check the solution by moving this box.

Example Try it first. Check the solution by moving this box.

Investigate

Energy stored in a spring k = spring constant, measure of spring’s stiffness

Energy stored in a capacitor

The energy stored in a capacitor is the ½ the product of the capacitance and the square of the voltage.

Example Try it first. Check the solution by moving this box.

Example Try it first. Check the solution by moving this box.

Bonus! Interesting insight from these relationships Energy density in space is proportional to the square of the electric field strength. Not just in capacitors, but everywhere: light, radio waves, and every other type of electromagnetism!