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Problem 17-9 Suppose a circuit has a resistance of 1000 in parallel with a capacitance of 1000 pF The frequency is 100 kHz If a wattmeter designed to read VA power shows a reading of 880 W, what is the true power This problem is rather complicated because the components are in parallel To begin, be sure the units are all in agreement so the formulas will work right Convert the frequency to megahertz: f = 100 kHz = 0100 MHz Convert capacitance to microfarads: C = 1000 pF = 0001000 F From the previous chapter, recall the formula for capacitive susceptance, and calculate it for this situation:

s 0 0

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35 STATE SPACE ANALYSIS (s2 + 2s + 2) (s + 2) 1 0 s(s + 2) s 0 0 2s s2 0 0 1 0 s(s + 1 + 1j)(s + 1 1j) 1 s s(s + 1 + 1j)(s + 1 1j)

The conductance of the resistor, G, is the reciprocal of the resistance, R, as follows: G = 1/R = 1/1000 = 0001000 S Now, use the formulas for calculating resistance and reactance in terms of conductance and susceptance in parallel circuits First, find the resistance: R = G/(G 2 + B 2) = 0001000/(00010002 + 00006282) = 0001000/0000001394 = 717 Then, find the reactance: X = B/(G 2 + B 2) = 0000628/0000001394 = 451 Next, calculate the phase angle: = arctan (X/R) = arctan ( 451/717) = arctan ( 0629) = 322 The power factor is found from the phase angle as follows: PF = cos = cos ( 322 ) = 0846 = 846% The VA power, PVA, is given as 880 W Therefore: PT = PF PVA = 0846 880 = 744 W

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which has a nite zero at s = 0 and n = 3 poles at s = 0, 1 + j, 1 j Engineers and analysts should be extremely careful with pole-zero cancelations In particular, a pole should never be canceled if it is in the right-half complex-plane and only with extreme caution if it is on the j -axis of the complex plane When a pole-zero cancelation occurs it only cancels for a speci c transfer function The order of that transfer function decreases, but the order of the state space representation remains n The a ect of the canceled pole will still appear in other transfer functions and in the transient response

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The visual interface between you and your computer is known as the display In desktop computers, an external display is often called a monitor There are two popular types in use for personal computing today A cathode-ray tube (CRT ) monitor resembles a television set without the tuning or volume controls This type of display is large and heavy, and although some people consider CRTs obsolete, other computer users prefer them, especially the larger ones, which can have a diagonal screen measure of 53 cm (21 in) or more A liquid crystal display (LCD) is lightweight and thin This type of display is used in notebook and portable computers It has become increasingly popular for desktop computers because the

ti This symbol represents the residual satellite clock error after performing the corrections described in C1 The satellite clock error is discussed in Section 842

i Ir This symbol represents the error due to dispersive atmospheric e ects described in Section 8441 i Tr This symbol represents the error due to non-dispersive atmospheric e ects described in Section 8442 i i M 1 , M 2 These symbols represent the pseudorange multipath errors on the L1 and L2 pseudorange measurements They are described in Section 847 i i 1 , 2 These symbols represent random measurement noise on the L1 and L2 pseudorange measurements They are discussed in Section 848

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