Physics 21 Fall, 2008 Solution to HW-19 31-6 A capacitance C and an inductance L are operated at the same angular frequency. (a) At what angular frequency will they have the same reactance? (b) If L =4 . 80 mH and C =3 . 70 µ F, what is the numerical value of the angular frequency in part (a)? (c) What is the reactance of each element? (a) Equate the reactances and solve for ω : 1 ωC = ωL ⇒ 1= ω 2 LC ⇒ ω = 1 √ LC . (b) Substituting numbers, ω = 1 p (4 . 80 × 10-3 )(3 . 70 × 10-6 ) =7 . 50 × 10 3 rad / s . (c) Again substituting numbers, 1 ωC = ωL =36 . 0Ω . 31-9 (a) What is the reactance of an inductor with an inductance of 3.40 H at a frequency of 84.0 Hz? (b) What is the inductance of an inductor whose reactance is 11.3 Ω at a frequency of 84.0 Hz? (c) What is the reactance of a capacitor with a capacitance of 3 . 56 × 10-6 F at a frequency of 84.0 Hz? (d) What is the capacitance of a capacitor whose reactance is 113 Ω at a frequency of 84.0 Hz? (a)
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This note was uploaded on 02/09/2009 for the course PHYS 021 taught by Professor Hickman during the Fall '08 term at Lehigh University .