DC Circuits

Chapter 17

Static charges will move if potential difference and conducting path exists between two points
Charged capacitor can discharge moving charges until potential on plates is equal
In solids, moving charges are electrons
In liquids and gases, both positive and negative ions can move
Electrolyte: substance whose aqueous solution conducts electric current
Positive charge moving one direction is equivalent to negative charge moving in opposite direction

Electrons pushed by electric field established in conductor
Electrons possess thermal velocity ~ 10⁶ m/s, causes random collisions with atoms
Speed due to electric field much less ~ 10^-3 m/s, called drift speed
Collisions create resistance to flow of charge

Due to collisions of conduction electrons with atoms
Unit is ohm (Ω); 1 ohm = 1V/1A
Circuit elements designed to provide measured amounts of resistance called resistors

For continuous current, need sustained potential difference and closed conducting path or circuit
Work must be done on charges to maintain potential difference; called emf
Old term was electromotive force
Unit: volt; symbol: script E

Electromagnetic: generator - creates emf through electromagnetic induction
Photoelectric: solar cell or photoelectric cell - uses photoelectric effect
Thermoelectric: thermocouple - temperature difference in dissimilar metals in contact produces potential difference
Piezoelectric: crystalline material which creates potential difference when distorted by pressure - used in microphones, acoustic instrument pickups
Chemical: battery - uses chemical reaction to transfer charges from one electrode to another

Battery is combination of cells connected in series, parallel, or combination of both
Cells in series: cells connected + to -, as in a flashlight
Battery emf = sum of cell emf's; battery current = current of one cell, the same throughout; battery resistance = sum of cell resistances
Cells in parallel: - terminals all connected together and + terminals all connected together
Battery emf = emf of one cell; total current drawn by circuit is divided equally among the cells; battery resistance is reciprocal of the sum of reciprocals of cell resitances

Circuit current is determined by emf of source and resistance in circuit.
E = IR where E is source emf, I is source current and R is total resistance in circuit
Internal resistance of battery must be included in total resistance
V = IR
Gives voltage drop across any resistance element in circuit

More than one conducting path for circuit current
Two or more components connected across two common points in circuit
Currents in parallel branches vary inversely with branch resistance; total current = sum of branch currents
Voltage drop the same across parallel branches
Parallel resistances add following reciprocal rule: reciprocal of total resistance equals sum of reciprocals of individual resistances

Algebraic sum of currents at any circuit junction equals zero; or currents into a junction equal currents leaving the junction; conservation of charge
Algebraic sum of all voltage drops around a circuit loop equals zero; conservation of energy

Combination of series and parallel
To analyze, first find total resistance, then total current
To simplify resistance networks, replace several resistances with one equivalent resistance
Start with series resistances and combine
Then collapse parallel branches into one equivalent resistance
Combine series resistances created by previous step
Continue until only one equivalent resistance remains

Resistance of uniform conductor directly proportional to its length, inversely proportional to its cross sectional area
Resistance increases with temperature increase for most metals
Resistance depends on nature of the material: the resistivity (ρ) has units of ohm·cm; R = r l/A
Range of Resistivities Low resistivity materials called conductors; most metals
High resistivity materials called insulators; nonmetals
In between are semiconductors: Si, Ge, B, Se; can act as conductors or insulators under certain circumstances

Discovered by Onnes (1908) while investigating low temp conductivity
Resistance drops suddenly to zero at critical temperature
Critical temp for most materials is a few kelvins, but newer composite materials found with higher temp superconductivity
Practical uses include MRI machines, levitating, high speed trains, research

Voltmeter-Ammeter method: measure current with ammeter, voltage drop with voltmeter, calculate resistance with Ohm's law; some error due to meters
Wheatstone bridge method: use resistance bridge and galvanometer, balance resistances so no current through galvanometer; more accurate than meters

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