
Circuit elements
 Current (I = ΔQ/Δt, sign conventions, units)

 Current is the rate of charge flow through the crosssection of a conductor (wire).
 Traditionally, the direction of current is taken as the flow of positive charges.
 The unit for current is Coulombs per second, C/s.
 Battery, electromotive force, voltage
 Electromotive force (emf) is really not a force, but a potential difference, with the unit voltage.
 A battery is a source of emf.
 If the battery has no internal resistance, then potential difference across the battery = EMF.
 If the battery has internal resistance, then potential difference across battery = EMF  voltage drop due to internal resistance.
 Terminal potential, internal resistance of battery

 Terminal potential is the voltage across the terminals of a battery.
 Internal resistance of a battery is like a resistor right next to the battery connected in series.
 Terminal potential = EMF  IR_{internal}
 Resistance
 Ohm's law (I = V/R)
 resistors in series

 I_{series} = I_{1} = I_{2} = I_{3}
 All resistors in series share the same current.
 V_{series} = V_{1} + V_{2} + V_{3}
 Voltage drop among resistors in series is split according to the resistance  greater resistance, greater voltage drop (V = IR).
 resistors in parallel

 V_{parallel} = V_{1} = V_{2} = V_{3}
 All resistors in parallel share the same voltage.
 I_{parallel} = I_{1} + I_{2} + I_{3}
 Current among resistors in parallel is split according to the resistance  greater resistance, less current (I = V/R).
 resistivity (ρ = RA/L)
 Resistivity is the inverse of conductivity.
 Greater resistivity, greater resistance of the material.
 Rearranging the above equation to get R = ρL/A. To make a wire of low resistance, select a material that has low resistivity, keep the wire short, and keep the diameter of the wire large.
 Extension cords are made really thick to keep the resistance down, so it doesn't heat up and cause a fire.
 Capacitance
 concept of parallelplate capacitor

 C = Q/V = εA/d
 Greater capacitance is created by a greater charge on plates (Q) for a given voltage (V), greater plate area (A), or smaller distance between plates (d).
 V = Ed, where V is voltage across capacitor, E is electric field between capacitor, and d is the distance between capacitor plates.
 energy of charged capacitor
 U = ^{Q2}/_{2C} = ½QΔV = ½C(ΔV)^{2}
 U is the potential energy of the charged capacitor, Q is charge stored (magnitude of either +Q or Q on one of the plates), C is capacitance.
 capacitors in series

 ^{1}/_{Ceq} = ^{1}/_{C1} + ^{1}/_{C2} + ^{1}/_{C3}
 capacitors in parallel

 C_{eq} = C_{1} + C_{2} + C_{3}
 dielectric
 Dielectric = nonconducting material.
 Inserting a dielectric between the plates of a capacitor increases the capacitance by either increasing Q (if V is constant) or decreasing V (if Q is constant).
 V = V_{0}/κ
 C = κC_{0}
 Discharge of a capacitor through a resistor
 Charge
 Discharge
 During the discharge of a capacitor, the capacitor acts as a battery and drives current flow, which decreases with time as the capacitor discharges.
 Conductivity theory
 Conductivity is affected by electrolyte concentration:
 No electrolyte, no ionization, no conductivity.
 Optimal concentration of electrolyte, greatest conductivity due to greatest mobility of ions.
 Too much electrolyte, ions are too crowded, less ion mobility, less conductivity.
 Conductivity is affected by temperature:
 In metals, conductivity decreases as temperature increases.
 In semiconductors, conductivity increases as temperature increases.
 At extremely low temperatures (below a certain critical temperature typically a few degrees above absolute zero), some materials have superconductivity  virtually no resistance to current flow, a current will loop almost forever under such conditions.
 Conductivity (σ) is the inverse of resistivity (ρ).
 Place a capacitor inside a solution, the solution will conduct a current between the plates of the capacitor, thus you can measure the conductivity of a solution using a capacitor.
Circuits
 Power in circuits (P = VI, P = I^{2}R)
 P = IV = I^{2}R
 P is power, I is current, V is voltage, R is resistance.
 Power companies try to save the amount of copper needed for power lines by using thinner wires, which makes R quite high.
 To minimize P dissipated by the wires, they minimize I by maximizing V. This is why power lines transfer electricity at high voltage.
Alternating Currents and Reactive Circuits
 Rootmeansquare current
 I_{rms} = ^{Imax}/_{√2} = 0.7 I_{max}
 Rootmeansquare voltage
 V_{rms} = ^{Vmax}/_{√2} = 0.7 V_{max}
 V_{rms} = I_{rms}R
 P_{avg} = I_{rms}V_{rms} = I^{2}_{rms}R

