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- 1. IT2001PAEngineering Essentials (1/2)Chapter 4 - Resistors in Parallel Circuits Lecturer Namelecturer_email@ite.edu.sg Aug 16, 2012Contact Number
- 2. Chapter 4 - Resistors in Parallel CircuitsLesson ObjectivesUpon completion of this topic, you should be able to: Apply Ohm’s Law to calculate voltages, currents and resistances in a parallel circuit. IT2001PA Engineering Essentials (1/2) 2
- 3. Chapter 4 - Resistors in Parallel CircuitsSpecific Objectives State the characteristics of parallel-connected resistors Calculate the current flow, voltage drops across the various resistors and the total resistance for parallel- connected resistors. Use the current divider rule to calculate the branch current flowing in a circuit consisting of 2 resistors in parallel. IT2001PA Engineering Essentials (1/2) 3
- 4. Chapter 4 - Resistors in Parallel CircuitsResistors in Parallel I1 R1 Two Resistors are connected in parallel Resistors are connected in I2 R2 parallel when the same voltage is applied across each resistor. I I1 & I2 are branch currents I V is the total current IT2001PA Engineering Essentials (1/2) 4
- 5. Chapter 4 - Resistors in Parallel CircuitsSome Examples of Parallel Circuits IT2001PA Engineering Essentials (1/2) 5
- 6. Chapter 4 - Resistors in Parallel CircuitsVoltage Across Resistors in Parallel The voltage across any branch of a parallel circuit is equal to the voltage across any of the other branches in parallel. IT2001PA Engineering Essentials (1/2) 6
- 7. Chapter 4 - Resistors in Parallel CircuitsVoltage Across Resistors in Parallel I1 R1 The voltage across each resistor is the same. I2 R2 I3 R3 V = V1 = V 2 = V 3 I V IT2001PA Engineering Essentials (1/2) 7
- 8. Chapter 4 - Resistors in Parallel CircuitsTwo Lamps Connected in Parallel x lamp 2 burned out lamp 1 lights If one lamp is up burned out , the other lamp is still working. supply voltage IT2001PA Engineering Essentials (1/2) 8
- 9. Chapter 4 - Resistors in Parallel CircuitsExample 4-1 Determine the voltage across each resistor in the figure Solution: The five resistors are in parallel, so the voltage drop across each one is equal to the applied source voltage. There is no voltage drop across the fuse V1= V2 = V3 = V4 = V5 =25V IT2001PA Engineering Essentials (1/2) 9
- 10. Chapter 4 - Resistors in Parallel CircuitsCurrent in a Parallel Circuit I1 R1 I2 R2 I = I 1 + I2 I V Total supply current = sum of branch currents IT2001PA Engineering Essentials (1/2) 10
- 11. Chapter 4 - Resistors in Parallel CircuitsExample 4-2 The branch currents in the circuit of the figure are known. Determine the total current IT. Solution The total current IT is the sum of the two branch currents. So the total current into point A is IT=I1+I2=5mA + 12mA = 17mA IT2001PA Engineering Essentials (1/2) 11
- 12. Chapter 4 - Resistors in Parallel CircuitsTotal Parallel Resistance When resistors are connected in parallel, the total resistance of the circuit decreases. The total resistance of a parallel circuit is always less than the value of the smallest resistor. The circuit in the figure shows a general case of ‘n’ resistors in parallel. Applying Ohms Law to the circuit, the total resistance is given by the equation: IT2001PA Engineering Essentials (1/2) 12
- 13. Chapter 4 - Resistors in Parallel CircuitsTwo Unequal Resistors in Parallel I1 R1 Effective resistance , R is given by I2 R2 1 1 + 1 = R R1 R2 R2 + R1 = R1 R2 R1 R2 PRODUCT R = = R2 + R1 SUM IT2001PA Engineering Essentials (1/2) 13
- 14. Chapter 4 - Resistors in Parallel CircuitsThree Resistors in Parallel Parallel network Equivalent circuit R1 RT R2 R3 The reciprocal of the equivalent resistance equals the sum of the reciprocals of the branch resistances. 1 1 1 1 = + + RT R1 R2 R3 IT2001PA Engineering Essentials (1/2) 14
- 15. Chapter 4 - Resistors in Parallel CircuitsEquivalent Resistance Parallel network Equivalent circuit R1 R R2 R3 Equivalent or Total resistance is smaller than the lowest individual resistance. IT2001PA Engineering Essentials (1/2) 15
- 16. Chapter 4 - Resistors in Parallel CircuitsEqual-Value Resistors in Parallel Another special case of parallel circuits is the parallel connection of several resistors having the same resistance value. Suppose there are ‘n’ number of resistors R1, R2, R3, …….Rn, all with equal resistance value of R each. Then total resistance is given by: IT2001PA Engineering Essentials (1/2) 16
- 17. Chapter 4 - Resistors in Parallel CircuitsCharacteristics of Parallel Circuit The voltage across each resistor is the same. Total current = Sum of individual current The reciprocal of the total resistance = sum of the reciprocal of each resistance Total resistance is smaller than the lowest individual resistance. IT2001PA Engineering Essentials (1/2) 17
- 18. Chapter 4 - Resistors in Parallel CircuitsExample 4-3 I1 R1 =1Ω Find the potential difference across each resistor and the currents flowing through I2 R2 =1Ω them. V = 10 V potential across each resistor I3 R3 =2Ω I1 = 10 / 1 = 10 A I I2 = 10 / 1 = 10 A I3 = 10 / 2 = 5 A 10V IT2001PA Engineering Essentials (1/2) 18
- 19. Chapter 4 - Resistors in Parallel CircuitsExample 4-4 Two resistors of 30Ω and 40Ω respectively are connected in a parallel. Find the total resistance. 1 1 + 1 OR = R R1 R2 R1 R1 R2 1 1 + 1 R = = R 30 40 R2 + R1 R2 1 = 0.0333 + 0.025 30 x 40 R R = 1 30 + 40 = 0.0583 R R = 17.14 Ω R = 17.15 Ω IT2001PA Engineering Essentials (1/2) 19
- 20. Chapter 4 - Resistors in Parallel CircuitsCurrent Divider Rule I1 R1 I R2 I1 = I I2 R2 R1 + R2 I1 R1 I R1 I2 = I R1 + R2 I2 R2 IT2001PA Engineering Essentials (1/2) 20
- 21. Chapter 4 - Resistors in Parallel CircuitsExample 4-5 I1 100 Ω I = 10 A 25 Ω Find I1 and I2 . I2 R2I1 = I I1 = [ 25 / (25 +100) ] x 10 = 2 A R1 + R2 R1I2 = I I2 = [ 100 / (25 +100) ] x 10 = 8 A R1 + R2 IT2001PA Engineering Essentials (1/2) 21
- 22. Chapter 4 - Resistors in Parallel CircuitsNext Lesson IT2001PA Engineering Essentials (1/2) 22

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