Electric current Physics 114 12/31/2018 Lecture V

Up to this point Static situation – charges are not moving Coulombs force = charge * electric field Deeper look in the properties of the electric field - Gauss’s law Potential energy= charge * electric potential Electric potential – integral of electric field Electric field = gradient of the electric potential Next – dymanics = moving charges = electric current 12/31/2018 Lecture V

Concepts Primary concepts: Electric current Resistor and resistivity Electric circuit 12/31/2018 Lecture V

Laws Ohm’s law Power in electric circuits 12/31/2018 Lecture V

Electric current - + A flow of charge is called an electric current Note: net charge =0 + - It is measured in ampere (A=C/s) Need free charge to have electric current. Use conductors. 12/31/2018 Lecture V

Skiing  electric circuit High PE High PE Low PE Low PE Skiers Charges go from points with high PE to low PE To complete the circuit need a device that brings you back to high PE: Ski lift Battery 12/31/2018 Lecture V

Electric circuit Need free charge  electric circuit must consist of conductive material (wires). Electric circuit must be closed. Battery supplies constant potential difference – voltage. e - Battery converts chemical energy into electric energy. Symbol for battery 12/31/2018 Lecture V

Electric circuit a). Will not work, Circuit is not closed b). Will not work, Circuit is at the same potential (+), no potential difference - voltage. c). Will work. 12/31/2018 Lecture V

Ohm’s law Electric current is proportional to voltage. Coefficient in this dependence is called resistance R Resistance is measured in Ohm (W = V/A) I R V 12/31/2018 Lecture V

Resistors First digit Second digit Multiplier Tolerance 2.5 x103 W +- 5%. 12/31/2018 Lecture V

Resistivity traffic  Electric current Long narrow street  high resistance Condition of the road  material property called resistivity r. r is measured in W m L – length of the conductor A – its area. 12/31/2018 Lecture V

Resistance and Temperature When electrons move through the conductor they collide with atoms: Resistivity grows with temperature ( more collisions) r0 – resistivity measured at some reference temperature T0 a – temperature coefficient of resistivity 12/31/2018 Lecture V

Resistance and Temperature When electrons move through the conductor they collide with atoms: Temperature of the conductor increases because of the current (through collisions) Electrical energy is transformed into thermal energy Resistors dissipate energy Power – energy per unit of time- (in W=J/s) dissipated by a resistor 12/31/2018 Lecture V

Electric power Electric energy can be converted into other kinds of energy: Thermal ( toaster) Light (bulbs) Mechanical (washer) Chemical Electric power (energy per unit of time): 12/31/2018 Lecture V

Test problem You have an open working refrigerator in your room. It makes your room A hotter B colder 12/31/2018 Lecture V

Test problem P=IV P=I2R P=V2/R A light bulb is connected to a battery. It is then cooled and its resistance decreased. Brightness is proportional to consumed power. The light bulb burns A Brighter B dimmer P=IV P=I2R P=V2/R 12/31/2018 Lecture V

Alternating current (AC) Voltage changes sign  current changes the direction I Req ~ 12/31/2018 Lecture V

Electric circuits: resistors Current in=current out I1=I2 No electrons are lost inside Resistors dissipate power (energy/time) P=I2R Drop of voltage over a resistor DV=-IR: V2=V1-IR I1,V1 R I2,V2 12/31/2018 Lecture V

Electric circuits: wires We assume that wire have very small resistance (R=0) Current in=current out I1=I2 Power dissipated in wires P=I2R=0 Drop of voltage over a resistor DV=-IR=0 V2=V1 From the point of electric circuit wires can be stretched, Bended Straightened Collapsed to a point without changing the electrical properties of the circuit I1,V1 I2,V2 I1,V1 I2,V2 I1,V1 I2,V2 12/31/2018 Lecture V

Electric circuit: battery Energy conservation Drop of voltage in electric circuit is always equal to voltage supplied by an external source (e.g. battery). Current (the effective flow of positive charge) goes from + to – Electrons (negative charge!) go from – to + I R1 R2 R3 V 12/31/2018 Lecture V

Electric circuits: branches Charge is conserved Current – what goes in, goes out I1 I I2 I I3 V 12/31/2018 Lecture V

Symbols Circuits can be rearranged: Wires with negligible resistance can be Stretched Bended Collapsed to a point 12/31/2018 Lecture V

Skiing  electric circuit a b Ski lift c Battery Cannot stop at b, must get to c – ski lift: V=V1+V2 - Net voltage drop in a circuit is always equal to the supplied voltage (e.g. battery) 12/31/2018 Lecture V

Series connection Charge conservation: I=I1=I2=I3 Ohm’s law V1=IR1; V2=IR2; V3=IR3 Energy conservation: qV=qV1+qV2+qV3 V=V1+V2+V3 IReq=IR1+IR2+IR3 Req=R1+R2+R3 12/31/2018 Lecture V

Parallel connection Charge conservation: I=I1+I2+I3 Energy conservation: V=V1=V2=V3 Ohm’s law: I1=V/R1; I2=V/R2; I3=V/R3 12/31/2018 Lecture V

DC circuits Series connection Parallel connection I=I1=I2=I3 V=V1+V2+V3 Req=R1+R2+R3 Parallel connection I=I1+I2+I3 V=V1=V2=V3 12/31/2018 Lecture V

< < Series vs parallel - I R1=R2=R3=R Req=3R I=V/(3R) I1=I2=I3=I=V/(3R) R1=R2=R3=R Req=R/3 I=3V/R I1=I2=I3=I/3=V/R < < Total current and individual currents are smaller in series connection. 12/31/2018 Lecture V

Series vs parallel - Req R1=R2=R3=R Req=3R R1=R2=R3=R Req=R/3 > Equivalent resistance is larger in series connection. 12/31/2018 Lecture V

< < Series vs parallel - P R1=R2=R3=R Req=3R I=V/3R  Pnet=V2/3R P1=I2R Pnet=IV Brightness proportional to power R1=R2=R3=R Req=3R I=V/3R  Pnet=V2/3R I1=V/3R P1=V2/9R R1=R2=R3=R Req=R/3 I=3V/R  Pnet=3V2/R I1=V/R  P1=V2/R < < Total and individual power consumptions are smaller in series connection. Light bulbs are brighter in parallel connection. 12/31/2018 Lecture V