EE103hw4%20sol

EE103hw4%20sol - Homework 4 Solutions 1 A) Using KCL 5 A -...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Homework 4 Solutions 1 A) Using KCL 5 A - 10 A - I1 = 0 I - I - I = 0 1 2 3 10 A + I 3 - 9 A = 0 9 A + I 2 - 5 A = 0 Solving yields I1 = -5 A I 2 = -4 A I = -1A 3 -2 A + I 2 + I1 = 0 - I - 7 A - 3 A = 0 2 B) 7 A + I 3 + I 4 = 0 2 A - I 4 - 4 A = 0 Solving I1 = 12 A I = -10 A 2 I 3 = -5 A I 4 = -2 A Vx = 10V 12V - Vx - 2V = 0 Solving 2. Using KVL 10 2V + 8V - 3I x = 0 I x = 3 A 20V + 25V - 8V - V1 = 0 V1 = 37V 3. Using KVL V1 - V2 - V3 = 0 Solving V2 = 28V 8V - 17V + V = 0 V = 9V 2 3 24V - V1 + V2 = 0 V1 = -1V 4. Using KVL -15V - V2 - V3 = 0 Solving V2 = -25V V - 10V = 0 V = 10V 3 3 5. 6 branches, 4 nodes, 3 loops 6. The initial 6 A are split in I1 and I2. To find these currents calculate the equivalent resistance to the right of the first 20 ohms resistor Req = {[(10//12)+20]//10}+10 = [(5.45+20]//10]+10 = 7.17+10 = 17.17 ohms Thus the current divider is I1 = 6 A To find i3 and i4 calculate the equivalent resistance after the 10 resistor Req = [(10//12)+20 = 25.45 ohms Thus the current divider is i3 = 3.23 A To find i5 and i6 calculate the current divider 17.17 = 2.77 A 17.17 + 20 i2 = 3.23 A 25.45 = 2.31A 25.45 + 10 i4 = 0.911A i5 = 0.911A 12 = 0.497 A 12 + 10 i6 = 0.414 A 2 Thus the power in the 12 ohms resistor is P = i6 R = 0.4142 12 = 2.05W 7. The equivalent resistance to the right of the first 0.1S resistor is Req = [(52//2)+10 = 11.92 ohms Thus the current divider is I = 1A Thus the voltage V = 0.543 A * 10 = 5.43 V 8. a) 10 = 0.456 A 11.92 + 10 i2 = 0.543 A ({( R // 4R ) + R + 2R // R} + 2R ) // 2R = 134 R = 1.165R 115 } b) ( 2 R + R ) // 2 R + R + R // 2 R + R // 2 R = ({ ) 58 R = 1.054 R 55 2R2 + R2 + 2R2 RA = RB = = 5R R 9. a 2R2 + R2 + 2R2 5 RC = = R 2R 2 20 20 + 20 100 + 100 20 = 220 20 B 20 20 + 20 100 + 100 20 RC = = 44 100 RA = RB = 10 10 + 10 30 + 30 10 = 70 10 C 10 10 + 10 30 + 30 10 RC = = 23.33 30 RA = RB = 100 10 + 10 100 + 100 100 = 120 100 D 100 10 + 10 100 + 100 100 RC = = 1200 10 RA = RB = 10 2R R 2R2 1 = = R 2R + R + R 4R 2 A R R R2 1 = = R R3 = 2R + R + R 4R 4 R1 = R2 = 130 10 = 5.41 130 + 100 + 10 130 100 = 54.16 B R2 = 130 + 100 + 10 10 100 = 4.16 R3 = 130 + 100 + 10 R1 = 20 20 = 2.85 20 + 20 + 100 20 100 = 14.28 C R2 = 20 + 20 + 100 20 100 = 14.28 R3 = 20 + 20 + 100 R1 = 110 110 = 35.58 110 + 110 + 120 120 110 = 38.82 D R2 = 110 + 110 + 120 120 110 = 38.82 R3 = 110 + 110 + 120 R1 = ...
View Full Document

Ask a homework question - tutors are online