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94年 - 94 地方政府特種考試_四等_天文:微積分#38544
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六、求
?(20 分)
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c.(5%) Refer to the following figure and prove the law of Cosines,
#471720
Problem 5 (20%) A plane wave is normally incident on a dielcctric slab of relative permitivity &, and thickness d. where), and λ0 is the free-space wavelength of the incident wave, as shown in Figure (e). If free-space exists on both sides of the slab, find the reflection cocfficient of the wave reflected from the front of the slab.
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Problem 6 (10%) A lossless transmission Iine is terminated with a 100 Ω load. If the standing wave ratio (SWR) on the line is 1.5, find the two possible values for the characteristic impedance of the line.
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Problem 7 (20%) An average power of 1 (kW) at 10 (GHz) is to be delivered to an antenna at the TElo mode by an air-filled metallic rectangular waveguide 1 (m) long and having sides a = 2.25 (cm) and b = 1 (cm). Assume that all the conductors are perfect electric conductors. Find the maximum values of the electric and magnetic field intensities within the waveguide.
#471723
(5%) A point charge Q exists at (0, d, 0) in space, as shown in Figure (a). Using Theory of image, a point charge of -Q exists at (0, -d, 0) symmetrically, as indicated in Figure (b). The dielectric constant of the space is εo. Write the electric intensities (Ex|y=0, Ey|y=0, and Ez|y=0) for a point on the ZX-plane in terms of (d and R), or (d and r), as indicated in Figure (b).
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(5%) What is the surface charge distribution on the ZX-plane? Sketch the distribution.
#471726
1.(10pt) A rechargcable battery is capable of delivering 100mA for 10 hours. How much charge can it release at that rate? If the terminal voltage is assumed as 3V, how much energy can the battery deliver?
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2. (10pt) Find v0 of the following circuit. Assume ideal OP amplifier.
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3.(10pt) A balanced Y-connected load is connected to the generator by a balanced transmission line with impedance of 0.1+j0.2Ω per phase. The load is rated at 500kW, 0.866 power factor lagging, 254Vms phase voltage. Find line current and line voltage of the generator, respectively?
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4.(10pt) Phase voltage and phase current of a load are given as v(t)=141cosotV, i()=14sin(ωt+30°) A. Find average power and reactive power of the load.
#471730