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9/30/13 Lecture VII 1

Physics 122

Electric current

9/30/13 Lecture VII 2

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

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9/30/13 Lecture VII 3

Concepts •  Primary concepts:

– Electric current – Resistor and resistivity – Electric circuit

9/30/13 Lecture VII 4

Laws

•  Ohm’s law •  Power in electric circuits

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9/30/13 Lecture VII 5

Electric current •  A flow of charge is called an

electric current

tQI ΔΔ= /

•  It is measured in ampere (A=C/s)

•  Need free charge to have electric current. Use conductors.

Note: net charge =0

+ +

+ + +

+ +

- -

-

-

-

- -

André-Marie Ampère 1775-1836

9/30/13 Lecture VII 6

Skiing ßà electric circuit

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

High PE High PE

Low PE

Low PE

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9/30/13 Lecture VII 7

Electric circuit •  Need free charge à electric circuit must consist of

conductive material (wires). •  Electric circuit must be closed. •  Battery supplies constant potential difference –

voltage.

• Battery converts chemical energy into electric energy.

e -

Symbol for battery

9/30/13 Lecture VII 8

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.

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•  Electric current is proportional to voltage

9/30/13 Lecture VII 9

•  Coefficient in this dependence is called resistance R

•  Resistance is measured in Ohm (Ω = V/A)

Ohm’s law

VI ∝ IRV =

R

V

I

Georg Simon Ohm 1789-1854

9/30/13 Lecture VII 10

Resistors

•  First digit •  Second digit •  Multiplier •  Tolerance •  2.5 x103 Ω +- 5%.

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9/30/13 Lecture VII 11

Resistivity •  traffic ßà Electric current •  Long narrow street ßà high resistance •  Condition of the road ßà material property called

resistivity ρ.

ALR ρ=

ρ is measured in Ω m L – length of the conductor A – its area.

ΔQ = ΔNe = nevAΔt

I = ΔQΔt

= nevA

j = I / A = nev

9/30/13 Lecture VII 12

Electron’s speed •  Copper wire, 3.2mm in diameter, carries 5.0A of

current. Estimate the speed of electrons?

N =M /m(one molecule)= ρCU1

V64u

1u =1.67 ⋅10−27kgρCU = 8.9 ⋅103kg /m3

n = N /V =8.9 ⋅103

64 ⋅1.67 ⋅10−27

= 8.3⋅1028m−3

Assume each atom donates one electron to the pool of free electrons:

j = I / A = 5.03.14 ⋅1.62 ⋅10−6

= 0.62 ⋅106A /m2

j = nev

v = jne

=0.62 ⋅106

8.3⋅10281.6 ⋅10−19= 4.7 ⋅10−5m / s

l = 4.7mt = l / v =105s =1.15days

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9/30/13 Lecture VII 13

Resistance and Temperature

•  When electrons move through the conductor they collide with atoms: –  Resistivity grows with temperature ( more collisions)

))(1( 00 TT −+= αρρ

ρ0 – resistivity measured at some reference temperature T0 α – temperature coefficient of resistivity

9/30/13 Lecture VII 14

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

RIP 2=

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9/30/13 Lecture VII 15

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):

IVP =

9/30/13 Lecture VII 16

•  You have an open working refrigerator in your room. It makes your room – A hotter – B colder

Test problem

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9/30/13 Lecture VII 17

•  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

Test problem

P=IV P=I2R P=V2/R

9/30/13 Lecture VII 18

Alternating current (AC) •  Voltage changes sign è current changes the direction

2/0VVrms =tVV ϖsin0= tϖsin0II =

eqRV /00I =Req I

tV ϖsin0

~

2/0IIrms =

RVRIP rmsrms /22 ==

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9/30/13 Lecture VII 19

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 ΔV=-IR: – V2=V1-IR

R I1,V1 I2,V2

9/30/13 Lecture VII 20

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 ΔV=-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

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9/30/13 Lecture VII 21

•  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 +

Electric circuit: battery 321 IRIRIRVVbattery ++=Δ=

R1

V

I R2 R3

9/30/13 Lecture VII 22

Electric circuits: branches •  Charge is conserved •  Current – what goes in, goes out

321 IIII ++=

V

I

I1

I3

I2 I