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free/or 0.5$ |
| 841 | A circuit shown in Fig. 3.53 has resistances R1 = 20 S and R2 = 30 S. At what value of the resistance Rx will the thermal power generated in it be practically independent of small variations of that resistance? The voltage between the points A and B is supposed to be constant in this case. |
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| 842 | In a circuit shown in Fig. 3.54 resistances R1 and R2 are known, as well as emf's ξ1 and ξ2. The internal resistances of the sources are negligible. At what value of the resistance R will the thermal power generated in it be the highest? What is it equal to? |
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| 843 | A series-parallel combination battery consisting of a large number N = 300 of identical cells, each with an internal resistance r = 0.3 S, is loaded with an external resistance R = 10 S. Find the number n of parallel groups consisting of an equal number of cells connected in series, at which the external resistance generates the highest thermal power. |
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| 844 | A capacitor of capacitance C = 5.00 μF is connected to a source of constant emf ξ = 200 V (Fig. 3.55). Then the switch Sw was thrown over from contact 1 to contact 2. Find the amount of heat generated in a resistance R1 = 500 Ω if R2 = 330 Ω. |
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| 845 | Between the plates of a parallel-plate capacitor there is a metallic plate whose thickness takes n = 0.60 of the capacitor gap. When that plate is absent the capacitor has a capacity C = 20 nF. The capacitor is connected to a de voltage source V = 100 V. The metallic plate is slowly extracted from the gap. Find: (a) the energy increment of the capacitor; (b) the mechanical work performed in the process of plate extraction. |
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| 846 | A glass plate totally fills up the gap between the electrodes of a parallel-plate capacitor whose capacitance in the absence of that glass plate is equal to C = 20 nF. The capacitor is connected to a do voltage source V = 100 V. The plate is slowly, and without friction, extracted from the gap. Find the capacitor energy increment and the mechanical work performed in the process of plate extraction. |
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| 847 | A cylindrical capacitor connected to a de voltage source V touches the surface of water with its end (Fig. 3.56). The separation d between the capacitor electrodes is substantially less than their mean radius. Find a height h to which the water level in the gap will rise. The capillary effects are to be neglected. |
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| 848 | The radii of spherical capacitor electrodes are equal to a and b, with a < b. The interelectrode space is filled with homogeneous substance of permittivity ε and resistivity ρ. Initially the capacitor is not charged. At the moment t = 0 the internal electrode gets a charge q0. Find: (a) the time variation of the charge on the internal electrode; (b) the amount of heat generated during the spreading of the charge. |
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| 849 | The electrodes of a capacitor of capacitance C = 2.00 nF carry opposite charges q0 = 1.00 mC. Then the electrodes are interconnected through a resistance R = 5.0 MS. Find: (a) the charge flowing through that resistance during a time interval t = 2.00 s; (b) the amount of heat generated in the resistance during the same interval. |
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| 850 | In a circuit shown in Fig. 3.57 the capacitance of each capacitor is equal to C and the resistance, to R. One of the capacitors was connected to a voltage V0 and then at the moment t = 0 was shorted by means of the switch Sw. Find: (a) a current I in the circuit as a function of time t; (b) the amount of generated heat provided a dependence I(t) is known. |
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| 851 | A coil of radius r = 25 cm wound of a thin copper wire of length l = 500 m rotates with an angular velocity ω = 300 rad/s about its axis. The coil is connected to a ballistic galvanometer by means of sliding contacts. The total resistance of the circuit is equal to R = 21 Ω. Find the specific charge of current carriers in copper if a sudden stoppage of the coil makes a charge q = 10 nC flow through the galvanometer. |
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| 852 | Find the total momentum of electrons in a straight wire of length l = 1000 m carrying a current I = 70 A. |
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| 853 | A copper wire carries a current of density j = 1.0 A/mm2. Assuming that one free electron corresponds to each copper atom, evaluate the distance which will be covered by an electron during its displacement L = 10 mm along the wire. |
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| 854 | A straight copper wire of length 1 = 1000 m and crosssectional area S = 1.0 mm2 carries a current I = 4.5 A. Assuming that one free electron corresponds to each copper atom, find: (a) the time it takes an electron to displace from one end of the wire to the other; (b) the sum of electric forces acting on all free electrons in the given wire. |
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| 855 | A homogeneous proton beam accelerated by a potential difference V = 600 kV has a round cross-section of radius r = 5.0 mm. Find the electric field strength on the surface of the beam and the potential difference between the surface and the axis of the beam if the beam current is equal to I = 50 mA. |
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| 856 | Two large parallel plates are located in vacuum. One of them serves as a cathode, a source of electrons whose initial velocity is negligible. An electron flow directed toward the opposite plate produces a space charge causing the potential in the gap between the plates to vary as cp = ax^(4/3), where a is a positive constant, and x is the distance from the cathode. Find:(a) the volume density of the space charge as a function of x; (b) the current density. |
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| 857 | The air between two parallel plates separated by a distance d = 20 mm is ionized by X-ray radiation. Each plate has an area S = 500 cm2. Find the concentration of positive ions if at a voltage V = 100 V a current I = 3.0 nA flows between the plates, which is well below the saturation current. The air ion mobilities are u0+= 1.37 cm2/(V•s) and u0- = 1.91 cm2/(V•s). |
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| 858 | A gas is ionized in the immediate vicinity of the surface of plane electrode 1 (Fig. 3.58) separated from electrode 2 by a distance L. An alternating voltage varying with time t as V = V0sinwt is applied to the electrodes. On decreasing the frequency co it was observed that the galvanometer G indicates a current only at w < w0, where co, is a certain cut-off frequency. Find the mobility of ions reaching electrode 2 under these conditions. |
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| 859 | The air between two closely located plates is uniformly ionized by ultraviolet radiation. The air volume between the plates is equal to V = 500 cm3, the observed saturation current is equal to Isat = 0.48 μA. Find: (a) the number of ion pairs produced in a unit volume per unit time; (b) the equilibrium concentration of ion pairs if the recombination coefficient for air ions is equal to r = 1.67*10-6 cm3/s. |
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| 860 | Having been operated long enough, the ionizer producing n'i = 3.5*109 cm-3*s-1 of ion pairs per unit volume of air per unit time was switched off. Assuming that the only process tending to reduce the number of ions in air is their recombination with coefficient r = 1.67*10-6 cm3/s, find how soon after the ionizer's switching off the ion concentration decreases η = 2.0 times. |
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