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Published byJoshua Ross Modified over 4 years ago

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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 Vsource = Va + Vb

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Resistance Equivalent resistance (effective resistance) for devices in a series circuit is sum of individual resistances R = R1 + R2 + R3 + …

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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 Icircuit = Vsource/Req

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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: R1=47Ω R2=82Ω V=45V Req = R1 + R2 Req = 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 Req = 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 R1= 400 Ω and R2 = 500 Ω are connected as a voltage divider. What is the voltage across R2?

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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/Req = 1/R1 + 1/R2 + 1/R3 … 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**

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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Quiz 1 a) Find the currents i1 and i2 in the circuit in the figure. b) Find the voltage vo. c) Verify that the total power developed equals the total power.

Quiz 1 a) Find the currents i1 and i2 in the circuit in the figure. b) Find the voltage vo. c) Verify that the total power developed equals the total power.

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