Chapter 27 IQ Questions - 27.2.1 Concepts in Ohm': Law...

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Unformatted text preview: 27.2.1 Concepts in Ohm': Law Given two conductors #1 and #2, they are of the same material. For i=1, 2, denote ° length: Li, 0 cross sectional area: Ai, ° applied voltage Vi: ° field inside : Hi 0 average drift velocity: vdi. V! Given: A2=Al, L2=2Ll, V1=V2=V. Find: Ratios E2!E1_ 3 E2/El 2 1 1/2 Hint: V=EL. J=UE=nqu Extra: Find delvdl. Explanation: EZJEI=(V2:’L2)I(V1:’L0:112. Extra: Same ohmic materials imply that 01:62 and nlznz. Or vdzivdl=J2IJl=(02E2)/(o1E1)=1/2. 27.5.1 Average collision time For an ohmic conductor, we have vdzat,a=£,andJ=nqu. m So the drift speed or the current density is proportional to E. This relation holds only if r is strictly constant. Estimate how much will 1: be changed, if vdrjfi is doubled, for a typical case where the average thermal speed is vth~103km/s, and average drift speed, vdlifi~10-4m/s. 1. It increases by more than 0.01%. It stays essentially the same, i.e. the change is less than 0.01%. 3. It decreases by more than 0.01%. Hint: The average speed of free electrons |V|=IVth + Vdrifil. Explanation: Based on vector the reader should convince himself/herself that the percentage of the maximum change 2v . —4 2X 10 _ dr'fl =—6=2><10 8% Vt}, 10 than 0.01% Ans=2. in v is less than . This is less 27.3.1 Thermal effect on resistivity Visualize free electrons moving through a crowded medium. They collide with the atoms along the way. As the temperature increases, what will happen to the average collision time, 1:? What will happen to the resistivity, p? Choose one: Hint: p = 2 where I is the collision time. nq r Explanation: When the temperature is increased, the atoms in the medium are "vibrating" with faster average speed. Free electrons will collide with atoms more frequently. So the average collision time I is decreased. The resistivity p=m/(nq2t), i.e. p is inversely proportional to 1:. As the collision time decreases, resistivity increases. Ans=2. 27.6.1 Power in two circuits case 2 V 3 identical bulbs are connected in two ways as shown. Determine PII/PI, where PI is the power ofper bulb in case I, and P11 is in case 11. Choose one: l P11/P1 | 9 . 2 Hmt: PZWZIQRZV Explanation: ...
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Chapter 27 IQ Questions - 27.2.1 Concepts in Ohm': Law...

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