1. SEE 1023 Circuit Theory Prepared by : jaafar shafie Superposition Examples

2. Superposition Principle The superposition principle states that the voltage across an element in a linear circuit is the algebraic sum of the voltage across that element due to each independent source acting alone. The superposition principle states that the current through an element in a linear circuit is the algebraic sum of the current through that element due to each independent source acting alone. OR

3. Superposition Principle + V a - 8  4  8  6  8  IaIa 1. Find V a and I a

4. Superposition Principle 1. 60 V Acting alone Va1 = -20V Ia1 = 625mA

5. Superposition Principle 2. 6A Acting alone Va2 = 16V Ia2 = 500mA

6. Superposition Principle 3. The whole Circuit Va = -4V Ia = 125mA

7. Superposition Principle 2. Find V a and I a - V a + 2V x 8  4  6  8  IaIa - + -Vx+-Vx+ 6A 60V

8. Superposition Principle 1. 60 V Acting alone + - Va1= -41.54 V Va1 Ia1= -5.385A

9. Superposition Principle 2. 6 A Acting alone + - Va2= 11.08 V Va2 Ia2= -3.231A

10. Superposition Principle 3. The Whole Circuit + - Va = -30.46 V Va Ia = -8.615A

11. CHAPTER 2: Tutorial 1. Use superposition to find V o 25 V 5 mA 2.2I x 4 k  20 k  + - VoVo IxIx

12. CHAPTER 2: Tutorial 2. Use superposition to find V o 8 V 2 A 3I x 6  3  IxIx + - VoVo + -

13. CHAPTER 2: Tutorial 3. Determine the maximum power delivered to the variable resistor R. (4-70) 40 V VxVx 3V x - + 6  5  15  R

14. CHAPTER 2: Tutorial 4. What resistor connected across terminals a-b will absorb maximum power from the circuit? What is that power? (4-71) 8 V 120V o 3 k  1 k  10 k  40 k  - + + - VoVo a b

15. CHAPTER 2: Tutorial 6. Determine the maximum power that can be delivered to the variable resistor R. (4-73) 60 V 10  20  5  25  R

16. CHAPTER 2: Tutorial 7. Determine the value of R such that the maximum power delivered to the R L is 3 mW (4-75) 1 V 2 V 3 V R R R RLRL

17. CHAPTER 2: Tutorial 8. Assume R Th can be varied while R L is fixed at 10 . what is the value of R Th so that maximum power can be transferred to R L. What is that power? 20 V 10  R Th

18. CHAPTER 2: Tutorial 9. Compute the value of R that results in maximum power transfer to the 10  resistor. Find that maximum power. 12 V 10  R 8 V 20 