Lesson_3.4 - Lesson 3.4 Direct Current circuits 1....

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Lesson 3.4 Direct Current circuits 1. Resistors in series. Resistors can be combined suitably to produce a larger or a smaller resistor than the ones that are available. A series connection is an end to end connection as shown below. V I I I I R 1 R 2 R 3 V 1 V 2 V 3 The figure shows three resistors, R 1 , R 2 and R 3 connected in series and connected to a source of potential V. Here V is the total potential drop across the three resistors. If V 1 , V 2 and V 3 are the potential drops across R 1 , R 2 and R 3 respectively, then V = V 1 + V 2 + V 3 But the current in each of the resistors is the same, namely, I Dividing the above equation by I we get 3 1 2 3 1 2 V V V V I I I I R R R R = + + = + + We connect resistors in series when we want a resistor larger than the ones that are available. Example 1: What is the resistance of a series combination of four 2.0 ohm resistances. Solution : R = 2 + 2 + 2 + 2 = 8
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2. Resistors in parallel When each resistor is connected across the same two points, we have a parallel connection as shown in the diagram below. V I I 1 I 2 I 3 R 1 R 2 R 3 A B Three resistors R 1 , R 2 and R 3 are connected across two points A and B across which a potential difference V is maintained. This means that the potential difference across R 1 = potential difference across R 2 = potential difference across R 3 = V. But the total current I reaching A is split into I 1 which passes through R 1 , I 2 which passes through R 2 and I 3 which passes through R 3 . So we can write: I = I 1 + I 2 + I 3 Dividing this equation by V which remains the same for all, we have 3 1 2 1 2 3 1 1 1 1 I I I I V V V V R R R R = + + = + + Resistors are connected in parallel when we need a resistance less than that are available. If two resistors R 1 and R 2 are in parallel, the equivalent resistance R is given by 1 2 1 2 R R R R R = +
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Example 2 : A 1.0 , a 2.0 and a 3.0 are connected in parallel. What is the total resistance of the circuit? Solution: 1 1 1 1 11 1 2 4 6 1 . 6 1 0 55 R R = + + = = Example 3 : The current in a loop circuit that has a resistance R 1 is 2.0 A. The current is reduced to 1.6 A when a resistor R 2 = 3.0 is added in series with R 1 . What is the value of R 1 ? Solution: If V is the potential difference across R 1 , then V = 2R 1 The total resistance when R 1 is connected in series with a 3.0 = R 1 + 3 Since the potential difference remains the same, we can write V = 1.6(R 1 + 3) 2R 1 = 1.6(R 1 + 3) 0.4 R 1 = 4.8 R 1 = 12 Example 4: A B 4 10 7 9 Find the total resistance between the points A and B Solution: First we find the equivalent resistance R of 7 and 10 in parallel: 7 10 70 4.1 7 10 17 R × = = = + Now we have a 4 , a 4.1 and a 9 are in series giving an equivalent resistance of 4 + 4.1 + 9 = 17.1
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Example 5: In the circuit in example 4, if the potential difference between A and B is 12.0 V, find the potential difference across each resistor and the
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This note was uploaded on 05/01/2011 for the course PHY 2049 taught by Professor George during the Spring '11 term at Edison State College.

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Lesson_3.4 - Lesson 3.4 Direct Current circuits 1....

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