Fall 2011 Homework 20 Solutions

Fall 2011 Homework 20 Solutions - Physics 21 Fall 2011...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 21 Fall, 2011 Solution to HW-20 31-21 You have a 207 Ω resistor, a 0 . 408 H inductor, a 4 . 99 μ F capacitor, and a variable-frequency ac source with an amplitude of 2 . 93 V. You connect all four elements to- gether to form a series circuit. (a) At what frequency will the current in the circuit be greatest? (b) What will be the current amplitude at this frequency? (c) What will be the current amplitude at an angular frequency of 410 rad/s? (d) At this frequency, will the source voltage lead or lag the current? (a) We need to look at the relationship V = IZ . Since V is ±xed, in order to maximize I we need to minimize Z . Z depends on ω via X L and X C : Z = r R 2 + ( X L - X C ) 2 Clearly, Z is minimized when X L - X C = 0. Using the de±nitions of X L and X C , 1 ωC = ωL ω 2 = 1 LC ω = 1 LC = 1 R (0 . 408 H) (4 . 99 μ F) = 701 rad / s (b) When X L - X C = 0, Z = R , so I = V Z = 2 . 93 V 207 Ω = 14 . 2 × 10 3 A (c) Now, X L - X C = (410 rad / s) (0 . 408 H) - 1 (410 rad / s) (4 . 99 μ F) = - 322 Ω I = V Z = 2 . 93 V r (207 Ω) 2 + ( - 322 Ω) 2 = 7 . 66 × 10 3 A (d) Since our calculation of X L - X C in part (c) came out
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/18/2011 for the course PHYS 021 taught by Professor Hickman during the Spring '08 term at Lehigh University .

Page1 / 2

Fall 2011 Homework 20 Solutions - Physics 21 Fall 2011...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online