DC Circuits
Chapter 19-20
Moving Charges
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
Electric Current
Rate of flow of electric charge through a cross section of a conductor
Unit is ampere (A or amp); 1A = 1C/s
Symbol for current is I ; I = Q/t
Since coulomb is large unit of charge, ampere is large current
Electrons flow from negative to positive potential;
Conventional current is opposite electron flow, assuming positive charges moving from
positive to negative
Movement of positive charges in one direction is equivalent to negative charges moving
in the opposite direction
Direct current: charges (electrons) move in one direction only: batteries supply direct
current
Alternating current: charges move back and forth, vibrating at the frequency of the AC
(60 Hz in USA). Power companies supply alternating current to homes and businesses
Electron Drift Speed
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
Resistance
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
EMF
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
Unit: volt; symbol: script E
Emf sources
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 that creates a potential difference when distorted by
pressure - used in microphones, acoustic instrument pickups, spark lighters
Chemical: battery - uses chemical reaction to transfer charges from one electrode to
another
Battery Cells
Wet cells: use liquid electrolyte - car battery
Dry cells: use paste “dry” electrolyte - flashlight batteries
Primary cells: replaced when reactants are used up
Storage cells: easily recharged
Fuel cells: New reactants added as needed
Dry Cell
Contain two electrodes and electrolyte
Anode: positive (electron poor) electrode
Cathode: negative (electron rich) electrode
Electrolyte carries electrons from anode to cathode
If outside circuit is connected, electrons move from cathode to anode
Emf of cell equal to work done moving charges from anode to cathode
Cell acts as electron pump, increasing potential energy of electrons
Output potential of cell equals emf when no external load is present
Emf depends on chemical reaction in cell
Combinations of Cells
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
Ohm’s Law
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
Series Circuits
Only one path for circuit current
Current the same in all circuit elements in series
Sum of voltage drops across circuit elements equals source emf
Total circuit resistance equals sum of separate resistances
Parallel Circuits
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 circuit elements or circuit branches
Parallel resistances add following reciprocal rule: reciprocal of total resistance equals
sum of reciprocals of individual resistances
Kirchhoff’s Rules for Circuit Analysis
1. Algebraic sum of currents at any circuit junction equals zero; or currents into a
junction equal currents leaving the junction; a consequence of conservation of
electric charge
2. Algebraic sum of all voltage drops around a circuit loop equals zero; or sum of
voltage drops through circuit elements equals voltage gains from batteries or other
emf sources. A consequence of conservation of energy
Circuit Networks
Combination of series and parallel circuit elements
To analyze, first find total resistance, then total current
To simplify resistance networks, combine several resistances and replace with one
equivalent resistance
Start with any 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
Now calculate total circuit current from battery and analyze circuit using Ohm’s law and
Kirchhoff’s laws
Resistance Laws
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 (rho), has units of
ohm·cm; R = ρ 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
Superconductivity
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
Resistance Measurements
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, but takes longer
Energy of Electric Current
Emf source does work on electrons
Electrons then do work on circuit components: resistors, bulbs, motors, etc.
One coulomb of charge moved through potential difference of one volt equals one joule
of work done, energy increase also 1J
W = qV = VIt (since q = It)
For one electron moved through 1 volt, unit of work/energy is electron volt (eV)
1 eV = 1.60 x 10-19 J
Energy and Resistance
Work done on resistance by current appears as heat; can be desirable (oven, iron, heater)
or not (motor, light, computer)
Since resistance always present in normal circuits, some energy lost due to heat
Joule’s Law: Q = I2Rt
Use to calculate heat produced by resistance and current over a time period
Power in Electric Circuits
Since power is work/time, P = VI
For a resistive element, P = I2R power dissipated in a resistance
If current is not known, P = V2/R
For total power in circuit, use E of emf source for V and RT of circuit for R
For maximum power transfer, RL = rsource
Power Companies
Energy sold in kilowatt-hours, a unit of energy (power x time)
1 kW-hr means device used 1000 watts of power for one hour
To minimize power loss in transmission lines, high voltages and fairly low currents are
used for long distance transmission
Voltage is reduced with transformers for use in homes
Home Electrical Circuits
Circuits in homes are in parallel; devices are connected are also in parallel
When many resistances are connected in parallel, total resistance is low, so current is
high
Too much current through wires causes excessive heating, fire hazard
Circuits protected from high currents by circuit breakers or fuses
Electric Safety
Current causes injury, not voltage
Usually, our bodies do not conduct current well so shock from line voltage not fatal
Currents can be high if skin conductivity is high -- wet or salty
Must be a potential difference for current to flow -- connection to high voltage not
dangerous unless path to ground exists
Grounded (3 wire) and polarized plugs help prevent shocks
Ground fault current interrupters (GFCI) should be used in wet locations