I = ΔQ/Δt.
Current is the rate of charge flow through the cross-section of a conductor (wire).
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.
Voltage across terminals of battery; EMF - IRinternal
Internal resistance of a battery is like a resistor right next to the battery connected in series.
V = IR
Resistors In Series
Iseries = I1 = I2 = I3.
All resistors in series share the same current.
Vseries = V1 + V2 + V3
Resistors in Parallel
Vparallel = V1 = V2 = V3.
All resistors in parallel share the same voltage.
Iparallel = I1 + I2 + I3
ρ = RA/L
For higher resistivity, keep wire with high resistance and high area and low length.
Concept of parallel-plate 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 a 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
Ceq = C1 + C2 + C3
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 = V0/κ
C = κC0
Discharge of a capacitor through a resistor
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: concentration of electrolytes
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 Theory: Temperature
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.
Power in Circuits
P = IV = I2R
To minimize P dissipated by the wires....
minimize I by maximizing V. This is why power lines transfer electricity at high voltage.
Root-mean-square current of AC
Irms = Imax/√2 = 0.7 Imax
Root-mean-square voltage of AC
Vrms = Vmax/√2 = 0.7 Vmax