4/8/2012. Example. Definition of the current: dq I = dt

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1 4/8/0 Whenever electric charges of like signs move under the influence of an alied of electric field, an electric current is said to exist The current is the rate at which the charge moves in the wire. Definition of the current: l The average current that asses any oint in a conductor during a time Δt is defined as ΔQ (7.) Δt where ΔQ is the amount of charge crosses the shaded area in a time Δt. The instantaneous current is dq dt (7.) The S.. Current unit is the amere ( ).often it is convenient to use the milliamere (m) m 0 lso μ 0 6 n C One amere of current is one coulomb er second:. s n a metallic conductor, the current is due to the motion of electrons, so the direction of the current will the oosite to the direction of flow of the electrons. Charges flow only if there is a otential difference. Something that rovides a otential difference is known as a voltage source.8x0 electrons ass through a oint in a wire in 4 minutes. What was the average current? av av ΔQ Ne Δt Δt 9 (.8 0 )(.6 0 ) ( 4 60) av.5

2 4/8/0 7. n electrochemical cell consists of two silver electrodes laced in an aqueous solution of silver nitrate. constant 0.5 current is assed through the cell for one hour, ) Find the total charge transorted through the cell in coulombs and in multiles of the electronic charge. B ) Each electrons reaching the cell discharges one ositively charged silver ion, which is then deosited on the negative electrode (cathode ). What is the total mass of the deosited silver?(the atomic mass of silver is 07.9 u., u kg) Solved in the course s text book The relation between the current in a wire with the density of conduction electrons and their drift velocity Let n be the number of mobile charge carriers er unit volume (the density of conduction electrons ) its unit is electron/m, The total number of charge carriers in the volume () of the conductor is N n.olume n..l where the olume. l Charge of one electron (the electronic charge ) e.6 x 0 9 C ΔQ [ number of ch arg es( N )] [ electronic charge ( e) ] Δ Q ne Δ Q ne av Δ t Δ t The drift seed, v d, is the seed at which the carriers move v av nev d (7.) d Δ t The current is the roduct of the electronic charge ( e ), the density of conduction electrons ( n ), the area ( ) and the drift velocity ( v d ) The current also deends on the resistance that the conductor offers to the flow of charge which is called electric resistance 7 Number coer wire is often used to wire house- hold electrical outlets. ts radius is mm 0 - m,if it carries a current of 0,what is the drift velocity of the electrons? ( metallic coer has one conduction electron er atom, the atomic mass of coer is 64 u, and the density of coer is 8900 Kg m - ), u.66 x 0-7 Kg The number of atoms er unit volume( n) x the mass of one atom (M ) the mass of a unit volume of coer The density (d ) d n M n d M 8900 Kg m electron / m (64 u)(.66 0 Kg u π r ( 0 6 ).4 0 m ν d.7 0 m / s nq (8.8 0 m )(.60 0 C )(.4 0 m )

3 4/8/0 Concetual questions These four wires are made of the same metal. ank in order, from largest to smallest, the electron currents a to d.. d > a > b > c B. b d > a c C. c > b > a > d D. c > a b > d E. b c > a d Concetual questions Suose a current-carrying wire has a cross-sectional area that gradually becomes smaller along the wire, so that the wire has the shae of a very long cone. How does the drift seed vary along the wire? (a) t slows down as the cross section becomes smaller. (b) t seeds u as the cross section becomes smaller. (c) t doesn t change. (d) More information is needed. (b). Under steady-state conditions, the current is the same in all arts of the wire. Thus, the drift velocity, given by v d / n e, is inversely roortional to the cross-sectional area T.Norah li lmoneef 9 7- esistance The electrical resistance of a conductor is the otential difference between its ends divided by the current The S.. unit of resistance is the ohm: esistances of kilohms and megohms are common: 6 kω 0 Ω, M Ω0 Ω. (7.4) Ohm s law Ω. Ohmic and Nonohmic Materials For many materials, the otential difference and the current are directly roortional,so the resistance is a constant indeendent of the current The ratio / is constant Materials with a constant resistance are said to obey Ohm s law and are called ohmic conductors 7. Find the resistance of the wire in figure 7. Solved in the course s text book Figure 7.. (a) coer wire has a variable otential difference between its end (b) the current varies linearly with the otential difference in the wire,so it is an ohmic conductor

4 4/8/0 Materials that do not follow Ohm s Law are called nonohmic materials, and have curved vs. grahs. Every ohmic material has a characteristic resistivity that deends on the roerties of the material and on temerature, i.e., resistivity is a roerty of substances Figure 7. the current versus otential difference grah for a rectifying transistor which roduces a large current in one direction, roduces only a small current in the oosite direction. This is an examle of a conductor that does not satisfy ohm s law deends on the material tye and shae resistance of a metal wire is directly roortional to its length, and inversely roortional to its cross-sectional area, : resistance (Ω) L ρ resistivity (Ω m) ρ L length (m) cross sectional area (m ) ρ σ conductivity σ ( Ω.m ) ρ ρ Thick wires have less resistance than thin wires. Longer wires have more resistance than short wires. f the conductivity of the material the wire is made of is high. then there will be less resistance. ( 7. 5 ) ( Ω.m ) ( 7. 6 ) Table 7. conductors semiconductors nsulators onic conductors esistivities in Ω m at 0 0 C substance esistivity { ρ } [Ω m] Silver.47x0 8 Cooer.7x0 8 luminum.6x0 8 Germanium 0.60 Silicon 00 Glass Sulfur 0 5 Body fluids arox Find the room temerature resistance of a coer wire 00 m long with a radius of mm 0 - m ( from table 7. ρ coer at room temerature( 0 0 C) is.7 x 0-8 Ω. m ) Solved in the course s text book Good conductors have low resistivities Good insulators have high resistivities 4

5 4/8/0 : small flashlight bulb draws 00 m from its.5 battery. (a) What is the resistance of the bulb? (b) f the voltage droed to., how would the current change?.5 5 Ω m 5 : otential difference is maintained across a.50-m length of tungsten wire that has a cross-sectional area of mm. What is the current in the wire? ( ).00 m mm m 000 mm 7 Δ ( )( m ) ρ 8 ( Ω m )(.50 m ) 6.4 Concetual questions cylindrical wire has a radius r and length L. f both r and L are doubled, the resistance of the wire (a) increases (b) decreases (c) remains the same nswer: (b). The doubling of the radius causes the area to be four times as large, so the resistance decreases. cylindrical coer rod has resistance. t is reformed to twice its original length with no change of volume. ts new resistance is: / Concetual question f a iece of wire has a certain resistance, which wire made of the same material will have a lower resistance? أسمك ) a thicker wire أطول B ) a longer wire ns: أرق C ) a thinner wire Concetual questions f the length of a wire increased, the current flow decreases because of the longer ath f the area of a wire increased, the current flow increases because of the wider ath ρ L/ f we change to a material with better conductivity, the current flow increases because charge carriers move better 5

6 4/8/0 Quiz f a current of 80.0 m exists in a metal wire, how many electrons flow ast a given cross section of the wire in 0.0 min? N.00x0 0 electrons Quiz small flashlight bulb draws 00 m from its.5- battery. (a) What is the resistance of the bulb? (b) (b) f the battery becomes weak and the voltage dros to., how would the current change? a ) 5.0 Ω. b ) the current will dro to 40 m. Quiz Birds resting on high-voltage ower lines are a common sight. The coer wire on which a bird stands is. cm in diameter and carries a current of 50. f the bird s feet are 4.0 cm aart, calculate the otential difference across its body. Δ 89 μ Quiz 4 Calculate the diameter of a.5 cm length of tungsten filament in a small light bulb if its resistance is Ω (The electrical resistivity of tungsten is 5.6 x0-8 Ω.m ) d 0.8 x0 - m verage current nstantaneous current Number of the electrons Magnitude of the current esistance of a conductor summary esistance is determined by the geometry and by the resistivity of the material Δ Q Δ t dq dt Δ Q N e av nev ρ d L Home work:, 0,, and 8 6

7 4/8/0 7.5 series and arallel resistors ;Kirchhoff s rules Statement of Kirchhoff s ules Junction ule ( 0) The sum of the currents entering any oint must equal the sum of the currents leaving that junction statement of Conservation of Charge in out Loo ule ( 0) The sum of the otential changes around any closed circuit loo must be zero You must go around the loo in one direction The sum of the measured will equal zero (a) (b) The voltage across a battery is taken to be ositive (a voltage rise) if traversed from to and and negative if traversed in the oosite direction. The voltage across a resistor is taken to be negative (a dro) if the loo is traversed in the direction of the assigned current and ositive if traversed in the oosite direction. ba ba Calculate the current flowing into the node in out ( ) - - The current flowing into the node is which is the same as flowing out of the node Calculate the current defined in the diagram - 4 (- 4 ) - 6 is in the oosite direction 6 ( 6 6 ) There are two ways to connect circuit elements. ) Series combination: Kirchhoff s rules :The sum of the otential changes around any closed circuit must be zero ly the Loo ule - The current is the same in resistors because any charge that flows through one resistor flows through the other but the otential differences across ( a ) them are not the same s s s ( b ) Figure 7 0 (a) three resistors in s ( 7. ) series ( b) the equivalent resistance s leads to the same current, 7

8 4/8/0 8 ) Parallel combination (a ) ( b ) ( ) 7. O that leaving must equal oint entering current the Figure 7. ( a ) three resistors in arallel. ( b ) the equivalent single resistance roduces the same current - B - B ) Parallel combination (a ) ( b ) ( ) 7. O that leaving must equal oint entering current the Figure 7. ( a ) three resistors in arallel. ( b ) the equivalent single resistance roduces the same current - B - B 7.0 (a ) find the equivalent resistance of the resistors in figure 7.0 a ( b ) the current in each resistor (a ) (b ) ( c ) Solved in the text book ) Find the current in the circuit shown in the figure. B ) Find the otential difference across each circuit element. solution n the figure,we had a kω, 0 kω, and 5 kω resistor in series. s k k 5 k 0 k Ω Ω Ω Ω s s

9 4/8/0 From the figure find ( a ) ( total current ), ( total resistance ) ( b ),, in out Ω Four resistors are connected as shown in figure. Find the equivalent resistance between oints a and c.. 4. B.. C..5. D E. Cannot determine from information given. Concetual questions From the circuit with source voltage and Total current, which resistor will have the greatest voltage across it? The resistor with the largest resistance (0 Ω) Which resistor has the greatest current flow through it? Same for all because series circuit f we re-ordered the resistors, what if any of this would change? Nothing would change 0Ω 0Ω 0Ω f we added a resistor in series with these, what would haen to the total resistance, total current, voltage across each resistor, and current through each resistor? Total resistance would increase Total current would decrease oltage across each resistor would decrease (ll voltage dros must still sum to total in series circuit; Kirchhoff s law of voltages) Current through each resistor would be lower (total current decreased, but same through each one) 9

10 4/8/0 Concetual questions from the circuit with source voltage and Total current, which resistor will have the greatest voltage across it? ll the same in arallel branches Which resistor has the greatest current flow through it? The ath of least resistance (0Ω) What else can you say about the current through each branch? They will sum to the total (currents sum in arallel circuits; Kirchhoff s law of current) f we added a resistor in arallel with these, what would haen to the total resistance, total current, voltage across each resistor, and current through each resistor? Total resistance would decrease Total current would increase oltage across each resistor would still be Current through each resistor would be higher and would sum to new total 7. Kirchhoff s rules in comlex circuits Kirchhoff s rules ermit us to analyze any dc circuit.including circuits too comlex Using the two rules () the sum of all the otential dros around any closed ath in a circuit is equal to zero. () The current entering any oint The current leaving. 7.5 Find the current in the circuit shown in the figure Solved in the text book Calculate Δ ab Δ ab 7 Δ ab if one battery is reversed? Δv ab 9v b a 0

11 4/8/0 Calculate the current in the circuit. i i Find the current, r and. Junction rule at a: 0 Loo (): r ( Ω)( )0 r /( ) 6 /( ) Ω Loo (): ( Ω)( ) ( Ω)( )0 5 (olarity is oosite!) Check with loo (): ( Ω)( ) ( Ω)( ) 0 5 Concetual questions Concetual questions What is the current in branch P? ) B) C) 5 D) 6 E) 0 The current entering the junction in red is 8, so the current leaving must also be 8. One exiting branch has, so the other branch (at P) must have 6. S 5 8 Junctio n 5 8 P P 6 Which of the equations is valid for the circuit below? Ω Ω ) 0 6 B) C) 4 0 Ω Ω D) E) 6 0

12 4/8/0 Quiz Calculate the currents,, and in the three branches of the circuit in the figure Kirchhoff s ules Junction ule Loo ule Series combination: Parallel combination: summary in out i i 0 s Home work 45,46,7