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Unformatted text preview: Direct Current Circuits 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. Three resistors, R 1 , R 2 and R 3 connected in series and connected to a source of potential V . V I I I I R 1 R 2 R 3 V 1 V 2 V 3 Three resistors, R 1 , R 2 and R 3 connected in series and connected to a source of potential V. V I I I I R 1 R 2 R 3 V 1 V 2 V 3 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: V = V 1 + V 2 + V 3 But the current in each of the V I I I I R 1 R 2 R 3 V 1 V 2 V 3 V = V 1 + V 2 + V 3 resistors is the same, namely, I Dividing this equation by I we have: If R is the total resistance of the combination, then: R = R 1 + R 2 + R 3 3 1 2 V V V V I I I I = + + V I R = Example 1: What is the resistance of a series combination of four 2.0 ohm resistances? R = R 1 + R 2 + R 3 + R 4 = 2 + 2 + 2 + 2 = 8 Ω Resistors in parallel V I I 1 I 2 I 3 R 1 R 2 R 3 A B When each resistor is connected across the same two points, we have a parallel connection . 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 . I I 1 I 2 I 3 R 1 R 2 R 3 A B 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 . I = I 1 + I 2 + I 3 V Dividing this equation by V : 3 1 2 I I I I V V V V = + + 1 2 3 1 1 1 1 R R R R = + + If R is the total resistance: V I R 1 R 2 B A 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 = + 1 2 1 1 1 R R R = + 1 2 1 2 R R R R + = Example 2: A 1.0 Ω , a 2.0 Ω and a 3.0 Ω are connected in parallel. What is the total resistance of the circuit? 1 2 3 1 1 1 1 R R R R = + + 1 1 1 1 2 3 = + + 11 6 = 6 Ω 11 R = Ω ≈ 0.55 Ω The total resistance is less than the smallest of the combined resistors. 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 Ω is added in series with R 1 . What is the value of R 1 ? If V is the potential difference across R 1 : V = 2R 1 R 1 2 A V R 1 1.6 A 3 V When a 3.0 Ω is connected in series with R 1 , the total resistance is: R 1 + 3 The current now is: I = 1.6 A The voltage V remains the same....
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 Spring '11
 George
 Physics, Current, Resistor, Potential difference, Ω, Series and parallel circuits

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