phys1112ch23solutions

phys1112ch23solutions - 187 ALTERNATING CURRENT CIRCUITS...

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Unformatted text preview: 187 ALTERNATING CURRENT CIRCUITS CHAPTER 23 ALTERNATING CURRENT CIRCUITS PROBLEMS _____________________________________________________________________________ _ 1. SSM REASONING AND SOLUTION The rms voltage can be calculated using V = IX C , where the capacitive reactance X C can be found using C 3 6 1 1 54 2 2 (3.4 10 Hz)(0.86 10 F) X f C π π- = = = Ω The voltage is, therefore, V IX = = Ω =- Χ Α 1 ς ( 29 ( 29 . 35 10 54 9 3 _____________________________________________________________________________ 4. REASONING The two capacitors, each of capacitance C and wired in parallel, are equivalent to a single capacitor C P that is the sum of the capacitances; C P = C + C = 2 C (Equation 20.18). The equivalent capacitance is related to the capacitive reactance X C of the circuit by Equation 23.2; ( 29 P C 1/ 2 C f X p = . We can determine X C by using Equation 23.1, C rms rms / X V I = , since the voltage and current are known. SOLUTION Since ( 29 P C 1/ 2 C f X p = and we know that C P = 2 C , the capacitance of each capacitor can be obtained as follows: P C C 1 1 2 or 2 4 C C C f X f X π π = = = Since the capacitive reactance is related to the voltage and current by C rms rms / X V I = , we have that ( 29 7 C rms rms 1 1 1 8.7 10 F 24 V 4 4 610 Hz 4 0.16 A C f X V f I p p p- = = = = 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 _____________________________________________________________________________ _ Chapter 23 Problems 188 6. REASONING The capacitance C is related to the capacitive reactance X C and the frequency f via Equation 23.2 as C = 1/(2 π fX C ). The capacitive reactance, in turn is related to the rms-voltage V rms and the rms-current I rms by X C = V rms / I rms (see Equation 23.1). Thus, the capacitance can be written as C = I rms /(2 π fV rms ). The magnitude of the maximum charge )....
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This note was uploaded on 04/14/2008 for the course PHY 1409 taught by Professor Vasut during the Spring '08 term at Baylor.

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phys1112ch23solutions - 187 ALTERNATING CURRENT CIRCUITS...

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