电容练习题(英文版).pdf

Tutorial Charge Current and Resistance 1 How many electrons are passing through a wire per second if the current is 1 00mA Answer I 10 3A q 1 6 10 19C let time t 1s and the number of electrons be n Using I Q t we have 1 00 10 3 n 1 6x10 19 1 n 6 25 1015 2 Calculate the mean velocity of electron flow the drift velocity in a wire where the free electron density is 5 0 1028m 3 if the current is 1 0A and the wire has a uni form cross section area of 1 0mm2 Answer I nqvA I 1A n 5 1028m 3 q 1 6 10 19C and A 10 6m2 3 In a certain semiconducting material the current carriers each have a charge of 1 6 10 19C How many are entering the semiconductor per second when the cur rent is 2 0 A Answer 4 How many free electrons are there per metre length of wire if a current of 2 0A re quires the electron drift velocity to be 10 3 ms 1 Answer 1 25 1022 electrons 5 A uniform copper wire of circular cross section has its current trebled and its diam eter doubled By what factor is the drift velocity of its free electrons multiplied as a result Answer n stays the same as the material is the same e stays the same as the electrons haven t changed 6 Find the steady current in a circuit when a charge of 40C passes in 5 0s Answer 8 0A 7 In a particular cathode ray tube the measured beam current is 30 0 A How many electrons strike the tube screen every 40 0s Answer 7 50 1015electrons 13 61928 ms10125 0 10106 1105 1 nqA I v 13 61928 ms10125 0 10106 1105 1 nqA I v 12 105 12 e I ntqne 1221 4 3 4 3 vv Ane I v neA I vnevAI 1 8 An aluminum wire having a cross sectional area of 4 00 10 6m2 carries a current of 5 00A Find the drift speed of the electrons in the wire The density of aluminum is 2 70g cm3 Assume each aluminum atom supplies one conduction electron Answer If the density of aluminium is 2 70g cm3 and each atom provides one free electron then if we find the number of aluminium atoms in 1 cm3 we ll also find the number of free electrons in 1 cm3 which is 106 n 0 130mm s Atomic mass number for Aluminium 27 Therefore there are NA atoms on 27g There fore in 2 7g there are NA 10 atoms But look at the density 2 7 g is 1cm3 Therefore there are NA 10 atoms in 1cm3 9 What is Ohm s law Answer The law states that the current I through a given conductor is proportional to the potential difference PD between its ends if temperature does not change V I constant 10 A light bulb has a resistance of 240 when operating with a potential difference of 120V across it What is the current in the light bulb Answer 0 5A 11 What is the difference between Ohmic materials and Nonohmic materials Answer Ohmic materials and devices have a linear current potential difference rela tionship over a large range of applied PD s The slope of the I versus V curve in the lin ear region yields a value for 1 R Nonohmic materials have a nonlinear current potential difference relationship these materials include semi conductors 12 A cylindrical wire has a radius r and length l If both r and l are doubled the re sistance of the wire a increases b decreases c remains the same Answer b The doubling of the radius causes the area A to be four times as large so the resistance decreases A A N N n 56 10 10 10 14 65 1030 1 10410 5 ms eNneA I vnveAI A 2 13 Calculate the resistance of an aluminum cylinder resistivity of aluminum 2 82 10 8 m that has a length of 10 0cm and a cross sectional area of 2 00 10 4m2 Repeat the calculation for a cylinder of the same dimensions and made of glass having a resistivity of 3 0 1010 m Answer For aluminum cylinder R l A 1 41 10 5 For glass R l A 1 5 1013 These answers tell us that it s MUCH easier for electrons to move through aluminium than glass 14 What is the resistan