Tiêu đề 03.Current-Electricity-f.pdf ✅

Physics Smart Booklet 3 Current Electricity Charges in motion constitute an electric current. A conductor offers a path for current. Application of potential difference across a conductor causes current. Potential difference can be provided using a cell or a battery (group of cells). Current in a circuit in a single direction is called a direct current (dc), while a current whose direction keeps reversing at regular intervals and whose magnitude keeps changing continuously is called alternating current (ac). Current carriers (mobile charge carriers): The charged particles whose drift in a definite direction constitutes the electric current are called current carriers. Conventional current in a metallic conductor: In metallic conductors, negatively charged particles, namely electrons, drift under the influence of applied potential difference. This constitutes an electron current. The direction of drift of positive charges is the direction of current. This current is called conventional current. The direction of conventional current is opposite to that of drift of electrons. Strength of electric current: Electric current is the net flow of charge per second across a surface. If Q is the amount of charge that passes through an area in a time interval t , then the average current in the given time interval is, av Q I t  =  . The instantaneous current is given by t 0 Q dQ I lim t dt  →  = =  If the current is steady, then Q I t = where Q is the charge flowing across a section of a conductor in an interval of time t. • The SI unit of current is ampere (A). 1 ampere = 1 coulomb per second. • Since 1 coulomb = 18 6.25 10  electrons, a flow of 18 6.25 10  electrons per second is equal to 1 ampere of current. Material Mobile charge carriers • Metallic conductors Free electrons • Liquid conductors Positive ions and Negative ions • Semiconductors Free electrons and Holes • Gaseous conductors Positive ions and free electrons • Super conductors Cooper pairs (a pair of electrons with opposite spins) Current density (J) • If current i is uniformly distributed over an area S and is perpendicular to it, then i j S = . • Current density is a vector quantity. The direction of current density is the same as the direction of motion of positive charges. • SI unit of current density is Am−2 . • Relation between current and current density is S i di j dS → ⎯⎯→ = =    over a finite area S.
Physics Smart Booklet 4 Drift velocity of free electrons • Drift velocity of electrons is given by e m = −  E vd where e → charge on the electron, m → mass of the electron, E → electric field,  → relaxation time. • The random speed of free electrons in a metallic conductor depends on the temperature and is of the order of 106 ms−1 . The drift speed of the free electrons is of the order of 10−4 ms−1 . Relaxation time and mean free path: The average time elapsed between two successive collisions of a free electron with the metal ions in a conductor is called relaxation time, denoted by . The average distance traveled by an electron between two successive collisions is called the mean free path, denoted by . Mobility () • The mobility () of charge carriers is given by d  = v / E and its unit is m2V −1 s −1 . • The mobility of electrons and conductivity of a material are related by the expression  = ne for a metallic conductor and e e h h  =  +  n e n e for a semiconductor where ne is electron density, nh is hole density, e is electron mobility, h is hole mobility. Expression for current and current density in terms of drift speed • d I nAev = and d J nev = where n is the number of electrons per unit volume of a metallic conductor of cross sectional area A and e is the charge on the electron. Ohm’s law: Mathematically Ohm’s law is expressed as V IR = where, R is a constant of proportionality called resistance of the conductor. • We have V R I = . The SI unit of resistance is ohm (). 1 ohm = 1 volt per ampere. • The dimensional formula is 2 2 3 [I M L T ] − − . At a given temperature, l R A  or R A = l where  = specific resistance or resistivity of the material of the conductor. 2 m R ne A A  =  =  l l where  is the specific resistance of the material and • For a conductor of length l having a circular cross-section, the resistance of the conductor is R ab  =  l (Here the radius of cross-section varies linearly from a to b and (b − a) << l). Resistivity or specific resistance () • The resistivity of a material is defined as numerically equal to the resistance across the opposite faces of a cube of the given material of unit length and unit area of cross section. • RA L = , R is in ohm, A is in square meter and L is in meter. • The SI unit of  is ohm meter ( m). The dimensional formula for  is 2 1 3 3 [I M L T ] − − . • The resistivity of a material is related to microscopic quantities by the relation, 2 m ne =  . • Resistivity of a conductor depends on the nature of the material and temperature.