p33_057

# P33_057 - 57(a The power factor is cos φ where φ is the phase constant deﬁned by the expression i = I sin(ωt − φ Thus φ = −42.0◦ and

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Unformatted text preview: 57. (a) The power factor is cos φ, where φ is the phase constant deﬁned by the expression i = I sin(ωt − φ). Thus, φ = −42.0◦ and cos φ = cos(−42.0◦ ) = 0.743. (b) Since φ < 0, ωt − φ > ωt. The current leads the emf. (c) The phase constant is related to the reactance diﬀerence by tan φ = (XL − XC )/R. We have tan φ = tan(−42.0◦ ) = −0.900, a negative number. Therefore, XL − XC is negative, which leads to XC > XL . The circuit in the box is predominantly capacitive. (d) If the circuit were in resonance XL would be the same as XC , tan φ would be zero, and φ would be zero. Since φ is not zero, we conclude the circuit is not in resonance. (e) Since tan φ is negative and ﬁnite, neither the capacitive reactance nor the resistance are zero. This means the box must contain a capacitor and a resistor. The inductive reactance may be zero, so there need not be an inductor. If there is an inductor its reactance must be less than that of the capacitor at the operating frequency. (f) The average power is Pavg = 1 1 Em I cos φ = (75.0 V)(1.20 A)(0.743) = 33.4 W . 2 2 (g) The answers above depend on the frequency only through the phase constant φ, which is given. If values were given for R, L and C then the value of the frequency would also be needed to compute the power factor. ...
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## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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