{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

14. Complex circuits-solutions

14. Complex circuits-solutions - gilvin(jg47854 14 Complex...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
gilvin (jg47854) – 14. Complex circuits – meyers – (21235) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. This homework is due Tuesday, March 29, at midnight Tucson time. 001 (part 1 of 2) 10.0 points The currents are ±owing in the direction in- dicated by the arrows. A negative current denotes ±ow opposite to the direction oF the arrow. Assume the batteries have zero inter- nal resistance. 9 . 9 Ω 19 . 4 Ω 4 V 15 . 4 V I I I ²ind the current through the 9 . 9 Ω resistor and the 4 V battery at the top oF the circuit. Correct answer: 1 . 9596 A. Explanation: Let : R 1 = 9 . 9 Ω , R 2 = 19 . 4 Ω , E 1 = 4 V , and E 2 = 15 . 4 V . R 1 R 2 E 1 E 2 I 1 I 2 I 3 At nodes, we have I 1 - I 2 - I 3 = 0 . (1) Pay attention to the sign oF the battery and the direction oF the current in the fgure. Us- ing the lower circuit in the fgure, we get E 2 + I 2 R 2 = 0 (2) so I 2 = -E 2 R 2 = - 15 . 4 V 19 . 4 Ω = - 0 . 793814 A . Then, For the upper circuit E 1 - I 2 R 2 - I 1 R 1 = 0 . (3) E 1 + E 2 - I 1 R 1 = 0 . I 1 = E 1 + E 2 R 1 = 4 V + 15 . 4 V 9 . 9 Ω = 1 . 9596 A . Alternate Solution: Using the outside loop -E 1 - E 2 + I 1 R 1 = 0 (4) I 1 = E 1 + E 2 R 1 . 002 (part 2 of 2) 10.0 points ²ind the current through the 19 . 4 Ω resistor in the center oF the circuit. Correct answer: - 0 . 793814 A. Explanation: ²rom Eq. (2) I 2 = - E 2 R 2 = - 15 . 4 V 19 . 4 Ω = - 0 . 793814 A . 003 10.0 points
Background image of page 1

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

View Full Document Right Arrow Icon
gilvin (jg47854) – 14. Complex circuits – meyers – (21235) 2 4 . 4 Ω 3 . 4 Ω 15 . 6 Ω 25 V 12 . 5 V Find the current through the 15 . 6 Ω lower- right resistor. Correct answer: 1 . 02459 A. Explanation: r 1 r 2 R E 1 E 2 A D E B C F i 1 i 2 I Let : E 1 = 25 V , E 2 = 12 . 5 V , r 1 = 4 . 4 Ω , r 2 = 3 . 4 Ω , and R = 15 . 6 Ω . From the junction rule, I = i 1 + i 2 . Applying Kirchhof’s loop rule, we obtain two equations: E 1 = i 1 r 1 + I R (1) E 2 = i 2 r 2 + I R = ( I - i 1 ) r 2 + I R = - i 1 r 2 + I ( R + r 2 ) , (2) Multiplying Eq. (1) by r 2 , Eq. (2) by r 1 , E 1 r 2 = i 1 r 1 r 2 + r 2 I R E 2 r 1 = - i 1 r 1 r 2 + I r 1 ( R + r 2 ) Adding, E 1 r 2 + E 2 r 1 = I [ r 2 R + r 1 ( R + r 2 )] I = E 1 r 2 + E 2 r 1 r 2 R + r 1 ( R + r 2 ) = (25 V) (3 . 4 Ω) + (12 . 5 V) (4 . 4 Ω) (3 . 4 Ω) (15 . 6 Ω) + (4 . 4 Ω) (15 . 6 Ω + 3 . 4 Ω) = 1 . 02459 A . 004 (part 1 of 2) 10.0 points An automobile battery has an em± o± 15 . 5 V and an internal resistance o± 0 . 116 Ω. The headlights have total constant resistance 4 . 95 Ω. What is the potential diference across the headlight bulbs when they are the only load on the battery? Correct answer: 15 . 1451 V. Explanation: Let : E = 15 . 5 V , R i = 0 . 116 Ω , and R h = 4 . 95 Ω . With the starter of, I h = E R i + R h = 15 . 5 V 0 . 116 Ω + 4 . 95 Ω = 3 . 05961 A Thus the voltage across the headlight bulbs is V = I h R h = (3 . 05961 A) (4 . 95 Ω) = 15 . 1451 V . 005 (part 2 of 2) 10.0 points What is the potential diference across the
Background image of page 2
gilvin (jg47854) – 14. Complex circuits – meyers – (21235) 3 headlight bulbs when the starter motor is op- erated, requiring an additional 46 A from the battery? Correct answer: 9 . 93127 V. Explanation: Let : I s = 46 A . R b R s R h The starter requires additional current, so I b = I h + I s .
Background image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 10

14. Complex circuits-solutions - gilvin(jg47854 14 Complex...

This preview shows document pages 1 - 4. Sign up to view the full document.

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