Current

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.

Terminal potential

Voltage across terminals of battery; EMF - IR_{internal}

Internal Resistance

Internal resistance of a battery is like a resistor right next to the battery connected in series.

Ohm's Law

V = IR

Resistors In Series

I_{series} = I_{1} = I_{2} = I_{3}.

All resistors in series share the same current.

Vseries = V_{1} + V_{2} + V_{3}

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}

Resistivity

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 = Q^{2}/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

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

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 = I^{2}R

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

I_{rms} = I_{max}/√2 = 0.7 I_{max}

Root-mean-square voltage of AC

V_{rms} = V_{max}/√2 = 0.7 V_{max}