Unit 3: Direct current nd electric resistnce Electric current nd movement of chrges. ntensity of current nd drift speed. Density of current in homogeneous currents. Ohm s lw. esistnce of homogeneous conductor of constnt cross section. Chnges in resistivity depend on temperture esistors ssocition. Series nd prllel ssocition. Joule heting Dischrging cpcitor
Electric current nd movement of chrges An electric current occurs when conductor is not in electrosttic equilirium. This cn e chieved y pplying n electric field 0 to the conductor. + + E + + q t ntensity is se quntity. Unit: Ampère is the sme for ny cross section of the conductor Although the moving prticles in conductor re electrons, for historicl resons electric current is studied s positive chrges moving in the direction of the electric field. Tipler, chpter 25, prt 25.
Electric current nd movement of chrges The chrges collide with the nuclei of the toms, cusing chotic movement. These collisions set up resistnce to the movement of the chrges (electric resistnce). V d An verge speed (drift speed V d ) cn e computed for the chrges, V d eing relted to E. This rte is clled moility (µ): µ v d E Drift speed is the modulus of vector drift velocity
Electric current nd movement of chrges A chrcteristic of ech conductor is the numer of free electrons per unit of volume (n) (density of chrge crriers), which depends on the chemicl structure of the mteril. Oviously, nd V d re relted through n: q t n q A v t d t n q A v d
Density of electric current in homogeneous currents. Current density (J) is the intensity of current through cross section of the conductor, divided into the section. This rte cn e computed t ny point of the cross section: nqavd J nqv d A A [J]L -2
Ohm s Lw r J is vector with the sme direction s E r t ny point: r J r E σ Omh s Lw r J E σ conductivity (Ωm) - Ω - S (Siemens) ρ/σ resistivity Ωm Mterils oeying Ohm s lw re clled ohmic mterils. Tipler, chpter 25, prt 25.2
Electric esistnce of homogeneous conductor of constnt cross section. A L dr A dr A dr J Edr Edr V V ρ σ σ σ r r Tipler, chpter 25, prt 25.2 E is lwys pointing to lower potentilsv >V )
esistnce of homogeneous conductor of constnt cross section. The quotient of the voltge pplied to conductor y the electric current flowing through such conductor is clled electricl resistnce nd depends on the mteril, shpe nd size of the conductor. []ML 2 T -3-2 V V ρ L A is mesured in Ohms
Chnges in resistivity depending on temperture The resistnce of conductors increses with temperture due to the higher numer of collisions etween free electrons nd nuclei. ρ ρ α [ + ( T 20ºC] 20 Tipler, chpter 25, section 25.2
Comintions of resistors. esistors in series. eq + + 2 3 +L n eq i i Tipler, chpter 25, section 25.4
Comintions of resistors. esistors in prllel. eq + 2 + 3 +L n eq i i
Joule heting Let s consider resistor (current from to ). ts terminls hve potentils V nd V (V >V ). Throughtime dt the chrge moving from to is: dqdt V V The energy lost on resistor y dq going from to is: du dq( V V) dt( V V) And the power (rtio of energy versus time): du P ( V V) V dt This energy is lost s heting in the conductor (Joule heting) due to the collisions etween chrges nd toms nuclei in the conductor. Tipler, chpter 25, section 25.3 2 V 2
Dischrging cpcitor f cpcitor chrged is connected to resistor, the stored energy on cpcitor is lost on resistor y Joule heting: i(t) i(t) d dt Q V 0 V (t) i(t) C V(t) From these equtions: V(t) C i(t) C d dt d C dt By integrting etweent0 (QCV 0 )nd time t: CV 0 d t 0 C dt V Ce 0 t C V(t) τ C C V e 0 t C Time constnt V (t τ) 0,37V 0 V (t 5τ ) 0,007V0 Tipler, chpter 25, section 25.6