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**OBJECTIVES After studying Chapter 6, the reader should be able to:**

Prepare for ASE Electrical/Electronic Systems (A6) certification test content area “A” (General Electrical/Electronic Systems Diagnosis). Identify a parallel circuit. Explain parallel circuit laws. Calculate voltage drops in a parallel circuit. State Kirchhoff’s current law.

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PARALLEL CIRCUITS A parallel circuit is a complete circuit that has more than one path for the current. The separate paths which split and meet at junction points are called branches, legs, or shunts.

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**KIRCHHOFF’S CURRENT LAW**

Kirchhoff’s current law (his first law) states: The current flowing into any junction of an electrical circuit is equal to the current flowing out of that junction. FIGURE 6-1 The amount of current flowing into junction point A equals the total amount of current flowing out of the junction.

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PARALLEL CIRCUIT LAWS Law 1 The total resistance of a parallel circuit is always less than that of the smallest-resistance leg. Law 2 The voltage is the same for each leg of a parallel circuit. Law 3 The sum of the individual currents in each leg will equal the total current.

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PARALLEL CIRCUIT LAWS FIGURE 6-2 The current in a parallel circuit splits (divides) according to the resistance in each branch.

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**DETERMINING TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

There are five methods commonly used to determine total resistance in a parallel circuit. Method 1 The total current (in amperes) can be calculated first by treating each leg of the parallel circuit as a simple circuit. FIGURE 6-3 In a typical parallel circuit, each resistance has power and ground and each leg operates independently of the other legs of the circuit.

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**DETERMINING TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

Method 2 If only two resistors are connected in parallel, the total resistance (RT) can be found using the formula RT (R1 x R2) / (R1 + R2). FIGURE 6-4 A schematic showing two resistors in parallel connected to a 12 volt battery.

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**DETERMINING TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

Method 3 A formula that can be used to find the total resistance for any number of resistances in parallel is 1 ÷ RT = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R FIGURE 6-5 A parallel circuit with three resistors connected to a 12 volt battery.

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**DETERMINING TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

Method 4 Instead of determining the lowest common denominator as in method 3, one can use the electronic calculator to convert the fractions to decimal equivalents.

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**DETERMINING TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

FIGURE 6-6 Using an electronic calculator to determine the total resistance of a parallel circuit. FIGURE 6-7 Another example of how to use an electronic calculator to determine the total resistance of a parallel circuit. The answer is ohms. Notice that the effective resistance of this circuit is less than the resistance of the lowest branch (20 ohms).

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**DETERMINING TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

Method 5 This method can be easily used when two or more resistances connected in parallel are of the same value. FIGURE 6-8 A parallel circuit containing four 12 ohm resistors. When a circuit has more than one resistor of equal value, the total resistance can be determined by simply dividing the value of the resistance (12 ohms in this example) by the number of equal-value resistors (4 in this example) to get 3 ohms.

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**PARALLEL CIRCUIT EXAMPLES Example 1**

FIGURE 6-9 Example 1.

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**PARALLEL CIRCUIT EXAMPLES Example 2**

FIGURE 6-10 Example 2.

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**PARALLEL CIRCUIT EXAMPLES Example 3**

FIGURE 6-11 Example 3.

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**PARALLEL CIRCUIT EXAMPLES Example 4**

FIGURE 6-12 Example 4.

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SUMMARY A parallel circuit, such as is used for all automotive lighting, has the same voltage available to each resistance (bulb). The total resistance of a parallel circuit is always lower than the smallest resistance. The separate paths which split and meet at junction points are called branches, legs, or shunts.

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SUMMARY Kirchhoff’s current law states: “The current flowing into any junction of an electrical circuit is equal to the current flowing out of that junction.” There are five basic methods that can be used to calculate the total resistance in a parallel circuit.

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REVIEW QUESTIONS Why is the total resistance of a parallel circuit less than the smallest resistance? Why are parallel circuits (instead of series circuits) used in most automotive applications? What does Kirchhoff’s current law state? What are three of the five ways to calculate the total resistance of a parallel circuit?

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CHAPTER QUIZ Two bulbs are connected in parallel to a 12 volt battery. One bulb has a resistance of 6 ohms and the other bulb has a resistance of 2 ohms. Technician A says that only the 2 ohm bulb will light because all of the current will flow through the path with the least resistance and no current will flow through the 6 ohm bulb. Technician B says that the 6 ohm bulb will be dimmer than the 2 ohm bulb. Which technician is correct? Technician A only Technician B only Both Technicians A and B Neither Technician A nor B

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CHAPTER QUIZ 2. Calculate the total resistance and current in a parallel circuit with three resistors of 4 , 8 , and 16 , using any one of the five methods (calculator suggested). What are the values? 27 ohms (0.4 ampere) 14 ohms (0.8 ampere) 4 ohms (3.0 amperes) 2.3 ohms (5.3 amperes)

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CHAPTER QUIZ 3. If an accessory such as an additional light is spliced into an existing circuit in parallel, what happens? The current increases in the circuit. The current decreases in the circuit. The voltage drops in the circuit. The resistance of the circuit increases.

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CHAPTER QUIZ 4. A 6-cylinder engine uses six fuel injectors connected electrically in two groups of three injectors in parallel. What would be the resistance if the three 12 ohm injectors were connected in parallel? 36 ohms 12 ohms 4 ohms 3 ohms

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CHAPTER QUIZ 5. A vehicle has four taillight bulbs all connected in parallel. If one bulb burns out (opens), the current flow in the circuit _____. Increases and the other bulbs get brighter Decreases because only three bulbs are operating Remains the same because all the bulbs are wired in parallel Drops to zero and the other three bulbs go out

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CHAPTER QUIZ 6. Two identical bulbs are connected to a 12 volt battery in parallel. The voltage drop across the first bulb is 12 volts as measured with a voltmeter. What is the voltage drop across the other bulb? 0 volt 1 volt 6 volts 12 volts

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CHAPTER QUIZ 7. Three resistors are connected to a 12 volt battery in parallel. The current flow through each resistor is 4 amperes. What is the value of the resistors? 1 ohm 2 ohms 3 ohms 4 ohms

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CHAPTER QUIZ 8. Two bulbs are connected to a 12 volt battery in parallel. Another bulb is added in parallel. Technician A says that the third bulb will be dimmer than the other two bulbs due to reduced current flow through the filament of the bulb. Technician B says that the amount of current flowing from the battery will decrease due to the extra load. Which technician is correct? Technician A only Technician B only Both Technicians A and B Neither Technician A nor B

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CHAPTER QUIZ 9. A vehicle has four parking lights all connected in parallel and one of the bulbs burns out. Technician A says that this could cause the parking light circuit fuse to blow (open). Technician B says that it would decrease the current in the circuit. Which technician is correct? Technician A only Technician B only Both Technicians A and B Neither Technician A nor B

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CHAPTER QUIZ 10. Three resistors are connected in parallel to a 12 volt battery. The total current flow from the battery is 12 amperes. The first resistor is 3 ohms and the second resistor is 6 ohms. What is the value of the third resistor? 1 Ω 2 Ω 3 Ω 4 Ω

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