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Ch. 25

Ch. 25. Electric Current and DC Circuits. Chapter Overview. Definition of Current Ohm’s Law Resistance – Conduction in Metals Kirchhoff’s Laws Analysis of DC Circuits RC Circuits. Current. Up to this point we have been concerned with charges that don’t move – Static

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Ch. 25

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  1. Ch. 25 Electric Current and DC Circuits

  2. Chapter Overview • Definition of Current • Ohm’s Law • Resistance – Conduction in Metals • Kirchhoff’s Laws • Analysis of DC Circuits • RC Circuits

  3. Current • Up to this point we have been concerned with charges that don’t move – Static • When charges do move, then an electric current flows • Current, usually denoted by the letter i is that rate at which charge moves. In other words how much charges flows past a point per time

  4. Current • i = current • q = charge • t = time • SI Units – ampere • Symbol A • Fundamental Unit (More on this later)

  5. The ampere is a fundamental unit, so the coulomb is a derived unit. Express the coulomb in terms of fundamental units • A/s • A·s • s/A • None of he above

  6. Batteries are often rated in amp·hours. What type of quantity does an amp∙hour represent? • Current • charge • Electric Potential • Capacitance • None of the above

  7. Ex. How many coulombs of charge are stored in 60 A·hr battery?

  8. Solution • i=Δq/Δt • Δq=iΔt • Δq=60 A x 1 hr • =60A x 1 hr x 3600 s/1 hr =216000 C

  9. Ex. 10000 protons fIow through a detector every .05 s. What is the current flowing through the detector?

  10. Soln. Protons • Current i=Δq/Δt • i=10000x1.602x10-19 C/.05 s • i= 3.2 x 10-14 A Detector

  11. Microscopic View of Current • At the microscopic level, current is made by individual charges moving at a speed vd in the material • A charge will travel the distance x in a time given by t = x/vd x vd q

  12. Microscopic view of current • The total amount of charge that flows through the gray shaded volume in time Δt is ΔQ = nqV where n is the number of charges per volume, V is the volume of the gray shaded area, and q is the charge of an individual charge • V = xA = vdΔtA • So ΔQ = nqvdAΔt

  13. Drift Velocity • I = ΔQ/Δt = nqAvd • vd is the drift velocity. It represents the average speed of charges in conductor • Ex. A copper wire has a radius of .50 mm. It carries a current of .25 A. What is the drift velocity of the electrons in the wire. Assume 1 free electron per atom. (ρcu = 8.93 g /cm3)

  14. There will be Avagadro’s number of charges in 1 mole of copper. the molar mass of copper is 63.5 g. The volume of 1 mole of copper is V = 63.5 g/8.93 g/cm3 = 7.31 cm3 = 7.31 x 10-6 m3

  15. n = NA / Vmol= 6.022 x 1023/7.31 x 10-6 m3= 8.24 x 1028 electrons /m3 vd = i/nqA = .25 A/(8.24 x 1028/m3 x 1.602 x 10-19 As x 3.14 x(5 x 10-4 m)2) = 2.4 x 10-5 m/s

  16. Ohm’s Law • What factors determine how much current will flow in a circuit (BRST)

  17. Ohm’s Law • Potential Difference and the material properties determine current that flows in a circuit

  18. Ohm’s Law • Current is proportional to potential difference • “Resistance” limits the amount of current that flows • Experimental Relationship found by Georg Simon Ohm • Not always true – e.g. diodes, transistors,…

  19. Resistance • Units – ohm denoted by Ω • What is the ohm in terms of V and A • What is the ohm in terms of fundamental units

  20. Units • Ω=V/A • Ω = kg m2 /(A2 s3 )

  21. Resistivity • What factors determine the resistance of a piece of metal? (BRST)

  22. Resistivity • Length – L • Cross sectional Area – A • resistivity ρ – material property (see table in text p. 792)

  23. Two different metals with different resistivities have the same length. Which metal will have the higher resistance? • The metal with the greater ρ • The metal with the smaller ρ • The resistances will be the same • Cannot be determined

  24. Temperature Dependence of Resistance • If you measure the resistance of a light bulb cold and then measure it when it is glowing, do you get the same resistance? (BRST)

  25. Temperature Dependence of Resistance • Resistance increases with increasing temperature for metals • It decreases with increasing temperature for semiconductors • For conductors R = R20(1 + α(T- 20 C°)) α is the Temperature coefficient of resistance (see p. 792)

  26. Ex. Find the temperature of the filament of a light bulb (assume W) by measuring the resistance when cold and glowing.

  27. Power • When we apply a potential difference across a resistor, it gets hot • What determines the power given off by a resistor?

  28. Power • Work = qΔV • Power = Work/time • P = qΔV/t but q/t = i • P = iΔV

  29. Power • Combine the expression for electric power P = iΔV with Ohm’s law ΔV = iR • P = iΔV = i2R = (ΔV )2/R

  30. Ex. A 100 W bulb is designed to emit 100 W when connected to a 120 V circuit. a) Draw a sketch and a schematic. b) What is the resistance of the bulb and the current drawn when connected to a 120 V outlet? c) Assuming the resistance doesn’t change, what would be the power output if the bulb was connected to a 240 V circuit?

  31. The electric bill • Power is a rate – it tells you how much energy per time is being used

  32. The electric company bills you in units of kw∙hr. What is a kw∙hr? (TPS) • It is a unit of power • It is a unit of energy • It is a unit of current • It is a unit of potential difference • Not enough information given

  33. The electric company bills you in units of kw∙hr. What is a kw∙hr? (TPS) • It is a unit of power • It is a unit of energy • It is a unit of current • It is a unit of potential difference • Not enough information given

  34. EX. How many joules are in a kW∙hr?

  35. It is the same It is greater at A It is greater at B It cannot be determined For the circuit shown below how does the current flowing through A compare to that flowing through B 3.0 Ω B A V 6.0 Ω

  36. You connect two identical resistors in series across a 6.0 V battery. How does the current in the circuit compare to that when a single resistor is connected across the battery • There is no difference • The current is twice as large • The current is ½ as large • Cannot be determined

  37. Resistors in Series • When we add resistors is series, the current decreases since the resistance increases • We define an equivalent resistance as a single resistor which produces the same current when attached to the same potential as the combination of resistors

  38. Series equivalent

  39. Equivalent Series Resistance • We want i to be the same • V= iReq • V1 = iR1, V2 = iR2, V3 = iR3 • V = V1 + V2 + V3 = iR1 + iR2 + iR3 • iR1 + iR2 + iR3 = i(R1 + R2 + R3) = iReq • So Req = R1 + R2 + R3

  40. Equivalent Series Resistance • How would this result change if there were four resistors in series? • In general as more resistors are added in series, the resistance increases so the current decreases

  41. Ex. a) Find the equivalent resistance for the following circuit. b) Find the current In the circuit c) Find the potential drop across each resistor d) Find the power dissipated by each resistor. e) Find the power Supplied by the power supply.

  42. You connect two identical resistors in parallel across a 6.0 V battery. How does the current supplied by the battery compare to that when a single resistor is connected across the battery? • There is no difference • The current is twice as large • The current is ½ as large • Cannot be determined

  43. Resistors in Parallel • When we add resistors is parallel, the current increases • The effective resistance must then decrease • How can that be? (BRST)

  44. Resistors in Parallel • There are more branches for current to follow in a parallel circuit, so current can be larger

  45. Resistors in Parallel • What is the same for the three resistors shown? (GR)

  46. Resistors in Parallel • The potential difference across each resistor is the same • Define i1 = V/R1, i2 = V/R2, i3 = V/R3 • How do the currents combine?

  47. Parallel Equivalent Resistance • We define the equivalent resistance as a single resistor that will draw the same current from the power supply

  48. Parallel Equivalent resistance • The currents add. Why? • i = i1 + i2 + i3 = V/R1 + V/R2 + V/R3 = V/Req

  49. a) Find the equivalent resistance. b) Find the current flowing through each resistor. c) Find the current supplied by the power supply

  50. Find the equivalent resistance for the following network

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