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Unformatted text preview: Chapter 26: Directcurrent circuits The current through the two resistors is the same. It is not “used up” as it flows around the circuit! These resistors are in series. eq 2 1 2 1 2 1 ) ( IR R R I IR IR IR IR = + = + = = ε ε §26.1 Resistors in series and parallel The pair of resistors R 1 and R 2 can be replaced with a single equivalent resistor provided that R eq = R 1 + R 2 . In general, for resistors in series ∑ = = + + + = n i i n R R R R R 1 2 1 eq K Current only flows around closed loops. When the current reaches point A it splits into two currents. R 1 and R 2 do not have the same current through them, they are in parallel. 2 2 1 1 = = R I R I ε ε The potential drop across each resistor is the same. At A: I =I 1 +I 2 (conservation of charge) eq 2 1 2 1 1 1 1 R R R I R R I = + = + = ε ε ε From the loop rules: 2 2 1 1 R I R I = = ε Substituting for I 1 and I 2 in the junction rule: In general, for resistors in parallel ∑ = = + + + = n i i n R R R R R 1 2 1 eq 1 1 1 1 1 K The pair of resistors R 1 and R 2 can be replaced with a single equivalent resistor provided that 2 1 eq 1 1 1 R R R + = Example: In the given circuit, what is the total resistance between points A and B? R 2 and R 3 are in parallel. Replace with an equivalent resistor R 23 Ω = + = 8 1 1 1 23 3 2 23 R R R R R 3 = 24 Ω R 2 = 12 Ω R 1 = 15 Ω A B R 23 =8 Ω R 1 = 15 Ω A B The resistors R 23 and R 1 are in series: eq 23 1 123 23 R R R R = Ω = + = The circuit can now be redrawn: B R 123 =23 Ω A Is the equivalent circuit and the total resistance is 23 Ω . Example continued Junction rule: The current that flows into a junction is the same as the current that flows out. (Charge is conserved) A junction is a place where three or more wires (or other components) meet. Loop rule: The sum of the voltage drops around a closed loop is zero. (Energy is conserved) §26.2 Kirchhoff’s Rules For a resistor: If you cross a resistor in the direction of the current flow, the voltage drops by an amount IR (write as –IR). There is voltage rise if you cross the other way (write as +IR). For batteries (or other sources of EMF): If you move from the positive to the negative terminal the potential drops by ε (write as – ε ). The potential rises if you cross in the other direction (write as + ε ). To solve multiloop circuit problems: 1. Assign polarity (+/) to all EMF sources....
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 Fall '07
 Fuchs
 Current, Energy, Resistor, Electric charge, Electrical resistance, Kirchhoff

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