Electricity Outline A. Electrostatics 1. Charge q is measured in coulombs 2. Three ways to charge something. Charge by: Friction, Conduction and Induction 3. Coulomb’s law for point or spherical charges: q1 q2 2 FE FE FE = kq1q2/r r 9 2 2 where k = 9.0 x 10 Nm /Coul 4. Electric field E = FE/qo (qo is a small, + test charge) F = qE Point or spherically symmetric charge distribution: E = kq/r2 E is constant above or below an ∞, charged sheet. 5. Faraday’s Electric Lines of Force rules: E 1. Lines originate on + and terminate on - _ 2. The E field vector is tangent to the line of force + 3. Electric field strength is proportional to line density 4. Lines are ┴ to conducting surfaces. 5. E = 0 inside a hollow or solid conductor 6. Electric potential difference (voltage): ΔV = W/qo We usually drop the Δ and just write V. Sometimes the voltage provided by a battery is know as the electromotive force (emf) ε 7. Potential Energy due to point charges or spherically symmetric charge distribution V= kQ/r 8. Equipotential surfaces are surfaces with constant voltage. The electric field vector is always to an equipotential surface. 9. Emax Air = 3,000,000 N/coul = 30,000 V/cm. If you exceed this value, you will create a conducting path by ripping e-s off air molecules. B. Capacitors 1. Capacitors A. C = q/V; unit of capacitance is the Farad = coul/volt B. For Parallel plate capacitors: V = E d C is proportional to A/d where A is the area of the plates and d is the plate separation. 2 C. Energy stored in cap = ½CV 3. Capacitors in Combination A. Capacitors in series (same charge): 1/Ceq = 1/C1 +1/C2 B. Capacitors in parallel (same voltage): Ceq = C1 + C2 1 C. Circuits 1. Water flow analogy 2. Current I = q / t units: 1 amp A = 1 coul/s 3. Ohm’s Law V = I R Ohmic resistors follow this law. Real resistors are approximately ohmic for restricted temperature ranges 4. Resistance R = r (L/A) where r is the resistivity of the material 5. Resistors: in series (same current): Req = R1 + R2 I R1 R1 V R2 R2 I in parallel (same voltage): 1/Req = 1/R1 + 1/R2 6. Power P = IV, P = I2R, P = V2/R units are Watts (1W = 1J/s) 10. Circuits with capacitors: uncharged cap acts like conducting wire, fully charged cap acts like a break in the circuit. 11. Loop rule: Sum of the voltages around any complete loop adds to 0. This is really just a statement of the conservation of energy. Remember that ΔV is negative when you follow current through a resistor. Vbat +Vbat – V1 –V2 = 0 R2 R1 12. Junction rule: Sum of currents into a junction = Sum of currents out of the junction. This is really just a statement of the conservation of charge. I2 I1 I1 + I2 = I3 I3 2 .