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Series Circuit Applied Physics and Chemistry Circuit Lecture 3

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Symbols Used

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Series Circuit in which current passes through all resistors Only one path for current Each resistor uses up some of the potential V source = V a + V b +....

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Resistance Equivalent resistance (effective resistance) for devices in a series circuit is sum of individual resistances R = R 1 + R 2 + R 3 + …

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Current Current in a series circuit is the source voltage divided by the equivalent resistance Current is the same everywhere in the circuit I circuit = V source /R eq

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Example Two resistors, 47Ω and 82Ω, are connected in series across a 45V battery. What is the current in the circuit? What is the voltage drop at each resistor? Known: R 1 =47Ω R 2 =82Ω V=45V R eq = R 1 + R 2 R eq = 47Ω + 82Ω = 129Ω

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Example Continued Current in the resistor: I = V/R I = 45V/129Ω = A Voltage at resistor 1: V = IR V=(0.349 A)(47Ω) = 16.4 V Voltage at resistor 2: V = IR V = (0.349 A)(82Ω) = 28.6 V

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Example Continued Will current increase, decrease or stay the same if the 47Ω resistor is replaced by a 37Ω resistor? New R eq = 37Ω + 82Ω = 119 Ω I = V/R = 45V/119Ω = A Current increases

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Example Continued What is the new voltage drop at resistor 2? V = IR V = (0.378 A)(82Ω) = 31V

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Series Circuit Uses Series circuit can be used as a voltage divider If a certain resistance needs a specific voltage, series circuit can be used to provide that Example p 406 A 9.0 V battery and two resistors R 1 = 400 Ω and R 2 = 500 Ω are connected as a voltage divider. What is the voltage across R 2 ?

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Parallel Circuits

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Parallel Circuit Multiple pathways for current Total current is the sum of the currents at each resistor (Current is NOT the same everywhere) Potential difference is the same everywhere in the circuit

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Parallel Circuit Equivalent resistance is reciprocal 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 … Placing resistors in parallel always decreases the equivalent resistance of the circuit

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Example Three resistors, 60Ω, 30Ω, and 20Ω, are connected in parallel across a 90V battery. Find the current through each branch of the circuit. Find the equivalent resistance. Find the current through the battery. Known: R1=60Ω R2=30Ω R3=20Ω V=90V

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Example Continued Current at R1: I=V/R I=90V/60Ω=1.5A Current at R2: I=V/R I=90V/30Ω=3 A Current at R3: I=V/R I=90V/20Ω=4.5 A Equivalent Resistance: 1/Req=1/60Ω + 1/30Ω + 1/20Ω = 6/60Ω Req= 10Ω Total Current: I=V/R I=90V/10Ω I=9 A

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Sample Circuits

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