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Basic Electric Circuits

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A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. Resistors in Series

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The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage. Resistors in Series

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From this we get the equivalent resistance (that single resistance that gives the same current in the circuit). Resistors in Series

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R T = 60 V T = 120 V I T = 2 A Simple Series Circuit Cut the resistor into three equal lengths and then separate. Resistors in Series

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R 1 = 20 R 2 = 20 R 3 = 20 V 1 = 40 V V 2 = 40 V V 3 = 40 V I 1 = 2 A I 2 = 2 A I 3 = 2 A I T = 2 A V T = 120 V R T = 60 Simple Series Circuit Resistors in Series

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12 V 1 2 3 + 2 A a b c d Voltage Drops Around a Series Circuit Resistors in Series

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2 1 3 12 V I = 2 A a bc dd 12 V 1 2 3 + 2 A a b c d Redraw Circuit Resistors in Series

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a bc dd 2 1 3 12 V 12 10 8 6 4 2 0 Voltage Drops I = 2 A Resistors in Series

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Direct-Current Circuits When two or more resistors are connected in series to a battery (A) the total voltage across the combination is the algebraic sum of the voltages across the individual resistors. (B) the same current flows through each resistor. (C) the equivalent resistance of the combination is equal to the sum of the resistances of each resistor. (D) all of the given answers

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Direct-Current Circuits As more resistors are added in series to a constant voltage source, the power supplied by the source (A) increases. (B) decreases. (C) does not change. (D) increases for a time and then starts to decrease.

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A parallel connection splits the current; the voltage across each resistor is the same: Resistors in Parallel

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The total current is the sum of the currents across each resistor: Resistors in Parallel This gives the reciprocal of the equivalent resistance:

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An analogy using water may be helpful in visualizing parallel circuits: If the pipes have different diameters, then different amounts of water flows through each. However, each has the same drop in height. Resistors in Parallel

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R T = 60 V T = 120 V I T = 2 A Parallel Circuit Cut the resistor in half and then separate. Resistors in Parallel

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R T = 60 I T = 2 A V T = 120 V Parallel Circuit Resistors in Parallel

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Adding Parallel Resistors Geometrically Find the equivalent Resistance 60 30 10 20 30 40 50 60 20 Resistors in Parallel

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Direct-Current Circuits Three identical resistors are connected in parallel to a 12-V battery. What is the voltage of any one of the resistors? (A) 36 V (B) 12 V (C) 4 V (D) zero

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Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it. For these circuits we use Kirchhoff’s rules. Some circuits cannot be broken down into series and parallel connections. At junction - a Kirchhoff’s Rules and Complex DC Circuits

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Direct Current Circuits Which diagram shows correct current direction in a segment of an electric circuit? (A) (B) (C) (D)

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Review of Chapter Equivalent resistance of resistors in series: Inverse of the equivalent resistance of resistors in parallel:

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