1. Physics 106 Lesson #16 Capacitors Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu

2. Review: Ohm’s Law The resistance of the resistor (light bulb) is R The voltage across the resistor is V The current through the resistor is I Ohm’s Law: I R Voltage = V I Assume perfect wire  NO voltage drop across wires! Ohms () Voltage = 0 I

3. Review: Adding Series Resistors For resistors R 1 & R 2 connected in series (sequentially), the current i passing through each resistor must be the same The voltages across R 1 & R 2 must add up to V → V = iR 1 + iR 2 = i(R 1 + R 2 ) = iR eq V +

4. Review: Adding Parallel Resistors Resistors R 1 & R 2 connected in parallel have the same potential difference (voltage) V across them The total current is the sum of the current through each resistor I = I 1 + I 2 = V/R 1 + V/R 2 = V(1/R 1 + 1/R 2 ) = V /R eq + V

5. Review: More Ways to Calculate Power Electric Potential Energy is transformed into to some other form (heat, light) by the resistor (light bulb). Power: Electric Potential (Energy) decreases across the light bulb (resistor) I R Voltage = V I Voltage = 0 I

6. Review: Superconductivity Zero Resistance The resistance of many (but not all) substances decreases with temperature A special class of materials known as superconductors lose all electrical resistance below a temperature known as the critical temperature Superconductors can levitate magnets by the Meissner Effect where a perfect conductor expels all magnetic fields from its interior

7. Capacitance Most objects can be charged and therefore store charge. Capacitance is charge stored per electric potential: Unit: Coulombs/Volt = Farads (for Michael Faraday)

8. Capacitance of a Parallel-Plate Capacitor For a parallel-plate capacitor, the capacitance is proportional only to geometric factors (the area of the plates A and the separation distance between them d ) and the natural constant   C is fixed at the factory!

9. Dielectrics Capacitance is increased by adding a dielectric (increase ε ) : More charge is stored per volt with larger ε compared to air Vacuum

10. Energy Stored in a Capacitor Units: Joules