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Resistors in Series and Parallel Circuits

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Resistors in circuits To determine the current or voltage in a circuit that contains multiple resistors, the total resistance must first be calculated. To determine the current or voltage in a circuit that contains multiple resistors, the total resistance must first be calculated. Resistors can be combined in series or parallel. Resistors can be combined in series or parallel.

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Resistors in Series When connected in series, the total resistance (Rt) is equal to: When connected in series, the total resistance (Rt) is equal to: Rt = R 1 + R 2 + R 3 +… The total resistance is always larger than any individual resistance. The total resistance is always larger than any individual resistance.

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Sample Problem 10 V 15 Ω 10 Ω 6 Ω Calculate the total current through the circuit. Rt = 15 Ω +10 Ω + 6 Ω Rt = 31 Ω I = V/R t = 10 V/ 31 Ω = 0.32 A

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Since charge has only one path to flow through, the current that passes through each resistor is the same. Since charge has only one path to flow through, the current that passes through each resistor is the same. The sum of all potential differences equals the potential difference across the battery. The sum of all potential differences equals the potential difference across the battery. Resistors in Series 10 V 5 V 3 V 2 V > R value = > V Value

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Resistors in Parallel When connected in parallel, the total resistance (Rt) is equal to: When connected in parallel, the total resistance (Rt) is equal to: 1/Rt = 1/R 1 + 1/R 2 + 1/R 3 +… Due to this reciprocal relationship, the total resistance is always smaller than any individual resistance. Due to this reciprocal relationship, the total resistance is always smaller than any individual resistance.

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Sample Problem 12 Ω 4 Ω 6 Ω Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω 1/R t = 6/12 Ω = ½ Ω Rt = 2 Ω

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Since there is more than one possible path, the current divides itself according to the resistance of each path. Since there is more than one possible path, the current divides itself according to the resistance of each path. smallest resistor = more current passes largest resistor = least current passes largest resistor = least current passes Resistors in Parallel

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The voltage across each resistor in a parallel combination is the same. The voltage across each resistor in a parallel combination is the same. Resistors in Parallel 10 V

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Calculate the total resistance in the circuit below +- 3 Ω 2 Ω 6 Ω 4 Ω R tot = 3 Ω + 2 Ω = 5 Ω R tot = 6 Ω + 4 Ω = 10 Ω 1/R tot = 2/10 Ω+ 1/10 Ω = 3/10 Ω R tot = 3 1/3 Ω

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