Electric (conduction) current I I According to general agreement its direction is chosen to coincide with the direction in which positive charge carriers would move, even if the actual carriers have a negative charge. a) Transport of charge; The SI unit of current is 1A (ampere). (1C=1A1s.) b) The electric current across a surface is defined as the rate at which charge is transferred through this surface

drift velocity The average velocity,, of charge carriers over a differential vicinity of a given location is called the drift velocity at this location. drift velocity The center of charge enclosed in this volume moves with the drift velocity.

current density The current density (associated with one type of charge carriers) is defined as a product of the drift velocity, the concentration of charge carriers and the charge of the carriers:

current density and current Current through a surface is equal to the flux of current density over that surface. dA vdvd  v d dt dQ = ? n The charge transferred through a differential surface dA in time dt The charge dQ transferred though the entire surface in time dt the current through the surface

electric current in a conductor In a conductor, current density is proportional to the electric field vector (Ohm's law) The constant of proportionality  is called the conductivity of the conductor. Under a steady flow of charged particles along a conductor, the current across any cross section of the conductor has the same value. I II We assign this value to the current in the conductor.

resistor A resistor is an electrical element with two sides for which (at any instant) the current passing through this element (any cross section) is proportional to the potential difference between its terminals. VaVa VbVb R I V a – V b = IR The proportionality coefficient R is called the resistance of the resistor. In SI 1  is the unit of resistance (1  =1V/1A).

construction of a resistor A resistivity

effect of temperature In a relatively wide range of temperatures the resistivity of a material is a linear function of temperature:  =  0 [1 +  (T-T 0 )] The proportionality coefficient  is called the temperature coefficient of resistivity. temperature resistivity metals semiconductors

resistors in series dQ I I VzVz VbVb VaVa Equivalent resistance of resistors connected in series is equal to the sum of the resistances of all resistors R s = R 1 + R 2 + … + R n

resistors in parallel V1V1 V2V2 The inverse of the equivalent resistance of resistors connected in parallel is equal to the sum of the inverses of resistances

electric power The rate at which the electric field performs work on the charged particles is called the electric power. The electric power delivered to an electrical element at instant t is equal to the product of the current flowing through this element and the voltage across this element at this instant. V1V1 V2V2 I dq

electric power dissipated in a resistor dQ I V1V1 V2V2 From Ohm's law (which is satisfied by all resistors) the electric power dissipated in a resistor can be determined also if the resistance of the resistor and either the current through or the voltage across the resistor is known.